ORIGINAL_ARTICLE
The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be generalized, improved, enriched and unified a number of recently announced results in the existing literature. Additionally, we elicit all of our main results by a non-trivial example and pose an interesting two open problems for the enthusiastic readers.
https://scma.maragheh.ac.ir/article_34322_c1a6f4a5bb424cbcce7290bf293886ca.pdf
2019-02-01
1
15
10.22130/scma.2018.89571.471
$b$-metric space
$wt$-distance
Fixed point
Orbitally $G$-continuous mapping
Kamal
Fallahi
fallahi1361@gmail.com
1
Department of Mathematics, Payame Noor University, Tehran, Iran.
LEAD_AUTHOR
Dragan
Savic
gagasavic98@gmail.com
2
Primary School ''Kneginja Milica", Beograd, Serbia.
AUTHOR
Ghasem
Soleimani Rad
gh.soleimani2008@gmail.com
3
Department of Mathematics, Payame Noor University, Tehran, Iran.
AUTHOR
[1] R.P. Agarwal, E. Karapinar, D. O'Regan, and A.F. Roldan-Lopez-de-Hierro, Fixed Point Theory in Metric Type Spaces, Springer-International Publishing, Switzerland, 2015.
1
[2] A. Aghanians and K. Nourouzi, Fixed points for Kannan type contractions in uniform spaces endowed with a graph, Nonlinear Anal. Model. Control., 21 (2016), pp. 103-113.
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[4] B. Bao, S. Xu, L. Shi, and V. Cojbasic Rajic, Fixed point theorems on generalized $c$-distance in ordered cone $b$-metric spaces, Int. J. Nonlinear Anal. Appl., 6 (2015), pp 9-22.
4
[5] F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. St. Ovidius. Constanta., 20 (2012), pp. 31-40.
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[6] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, 2008.
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[7] M. Bota, A. Molnar, and C. Varga, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory., 12 (2011), pp. 21-28.
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[8] Y.J. Cho, R. Saadati, and S.H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011), pp. 1254-1260.
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[9] Lj.B. Ciric, On contraction type mappings, Math. Balkanica., 1 (1971), pp. 52-57.
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[10] A.S. Cvetkovic, M.P. Stanic, S. Dimitrijevic, and S. Simic, Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory Appl., (2011), 2011:589725.
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[11] S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), pp. 5-11.
11
[12] K. Fallahi, $G$-asymptotic contractions in metric spaces with a graph and fixed point results, Sahand Commun. Math. Anal., 7 (2017), pp. 75-83.
12
[13] K. Fallahi, A. Petrusel, and G. Soleimani Rad, Fixed point results for pointwise Chatterjea type mappings with respect to a $c$-distance in cone metric spaces endowed with a graph, U.P.B. Sci. Bull. (Series A)., 80 (2018), pp. 47-54.
13
[14] K. Fallahi and G. Soleimani Rad, Fixed point results in cone metric spaces endowed with a graph, Sahand Commun. Math. Anal., 6 (2017), pp. 39-47.
14
[15] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), pp. 1467-1475.
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[16] N. Hussain, R. Saadati, and R.P. Agrawal, On the topology and $wt$-distance on metric type spaces, Fixed Point Theory Appl., (2014), 2014:88.
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[17] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), pp. 1359-1373.
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[18] O. Kada, T. Suzuki, and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44 (1996), pp. 381-391.
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[19] Z. Kadelburg and S. Radenovic, Coupled fixed point results under tvs-cone metric spaces and $w$-cone-distance, Advances Fixed Point Theory and Appl., 2 (2012), pp. 29-46.
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[20] M.A. Khamsi and N. Hussain, $KKM$ mappings in metric type spaces, Nonlinear Anal., 73 (2010), pp. 3123-3129.
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[21] A. Petrusel and I.A. Rus, Fixed point theorems in ordered $L$-spaces, Proc. Amer. Math. Soc., 134 (2006), pp. 411-418.
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[22] G. Soleimani Rad, H. Rahimi, and C. Vetro, Fixed point results under generalized $c$-distance with application to nonlinear fourth-order differential equation, Fixed Point Theory., in press.
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[23] W.A. Wilson, On semi-metric spaces, Amer. Jour. Math., 53 (1931), pp. 361-373.
23
ORIGINAL_ARTICLE
$C$-class Functions and Common Fixed Point Theorems Satisfying $\varphi $-weakly Contractive Conditions
In this paper, we discuss and extend some recent common fixed point results established by using $\varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalizes several existing onesin literature.We finally propose three open problems.
https://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdf
2019-02-01
17
30
10.22130/scma.2018.59792.211
Common fixed point
$varphi $-weakly contractive conditions
Complete metric space
Weakly compatible mappings
$C$-class function
Arslan
Hojat Ansari
analsisamirmath2@gmail.com
1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
AUTHOR
Tatjana
Dosenovic
tatjanad@tf.uns.ac.rs
2
Faculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.
LEAD_AUTHOR
Stojan
Radenovic
radens@beotel.net
3
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.
AUTHOR
Jeong Sheok
Ume
jsume@changwon.ac.kr
4
Department of Mathematics, Changwon National University, Changwon, 641-773, Korea.
AUTHOR
[1] M. Abbas and D. Doric, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat 24 (2010), pp. 1-10.
1
[2] M. Abbas and M.A. Khan, Common fixed point theorem of two mappings satisfying a generalized weak contractive condition, Int. J. Math. Math. Sci., Article ID 131068 (2009), pp. 1-9.
2
[3] R.P. Agarwal, R.K. Bisht, and N. Shahzad, A comparison of various noncommuting conditions in metric fixed point theory and their applications, Fixed Point Theory Appl., 1 (2014), pp. 1-33 .
3
[4] Lj. Ciric, Generalized contractions and fixed point theorems, Pub. Inst. Math., 12 26 (1971), pp. 19-26.
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[5] D. Doric, Common fixed point for generalized $varphi ,psi $-weak contractions, Appl. Math. Lett., 22 (2009), pp. 1896-1900.
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[6] T. Dosenovic, M. Postolache, and S. Radenovic, On multiplicative metric spaces, Survey, Fixed Point Theory Appl., 92 (2016), pp. 1-17.
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[7] T. Dosenovic, and S. Radenovic, Some critical remarks on the paper: ''An essential remark on fixed point results on multiplicative metric spaces'', J. Adv. Math. Stud., 10 (2017), pp. 20-24.
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[8] P.N. Dutta and B.S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., Article ID 406368 (2008), pp. 1-8.
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[9] D. Gopal, M. Imdad, and M. Abbas, Metrical common fixed point theorems without completeness and closedness, Fixed Point Theory Appl., 1 (2012), pp. 1-9.
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[10] J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear Anal., 74 (2011), pp. 768-774.
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[11] M. Jleli, V.'C. Rajic, B. Samet, and C. Vetro, Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations, J. Fixed Point Theory Appl., 12 (2012), pp. 175–-192.
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[12] G. Jungck and B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), pp. 227-238.
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[13] A. Latif, H. Isik, and A.H. Ansari, Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings, J. Nonlinear Sci. Appl., 9 (2016), pp. 1129-1142.
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[14] Z. Liu, Compatible mappings and fixed points, Acta Sci. Math., 65 (1999), pp. 371-383.
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[15] Z. Liu, X. Zhang, J.S. Ume, and S.M. Kang, Common fixed point theorems for four mappings satisfying $psi $-weakly contractive conditions, Fixed Point Theory Appl., 20 (2015), pp.1-22.
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[16] S. Moradi, Z. Fathi, and E. Analouee, The common fixed point of single-valued generalized $f-$weakly contractive mappings, Appl. Math. Lett., 24 (2011), pp. 771-776.
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[17] Z. Mustafa, H. Huang, and S. Radenovic, Some remarks on the paper ''Some fixed point generalizations are not real generalizations'', J. Adv. Math. Stud., 9 (2016), pp. 110-116.
17
[18] Z. Mustafa, M.M.M. Jaradat, A.H. Ansari, B.Z. Popovic, and H.M. Jaradat, $C-$class functions with new approach on coincidence point results for generalized $(psi, phi)-$weakly contractions in ordered $b-$metric spaces, SpringerPlus, 5 (2016), pp. 1-18.
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[19] L. Pasicki, Fixed point theorems for contracting mappings in partial metric spaces, Fixed Point Theory Appl., 185 (2014), pp. 1-16.
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[20] D.K. Patel, P. Kumam, and D. Gopal, Some discussion on the existence of common fixed points for a pair of maps, Fixed Point Theory Appl., 1 (2013), pp. 1-17.
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[21] O. Popescu, Fixed points for $varphi, $$psi $-weak contractions, Appl. Math. Lett., 24 (2011), pp. 1-4.
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[22] S. Radenovic, and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comp.Math. Appl., 60 (2010), pp. 1776-1783.
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[23] S. Radenovic, Z. Kadelburg, D. Jandrlic, and A. Jandrlic, Some results on weakly contractive maps, Bulletin of the Iranian Mathematical Society, 3 (2012), pp. 625-645.
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[24] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), pp. 257-290.
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[25] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), pp. 2683-2693.
25
ORIGINAL_ARTICLE
Common Fixed Point Theory in Modified Intuitionistic Probabilistic Metric Spaces with Common Property (E.A.)
In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and the common property (E.A.) in modified intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.
https://scma.maragheh.ac.ir/article_30018_01319582d03c748575cc8fcb9b401e9c.pdf
2019-02-01
31
50
10.22130/scma.2018.30018
Modified intuitionistic probabilistic Menger metric space
Property (E.A.)
Common property (E.A.)
Hamid
Shayanpour
h.shayanpour@sci.sku.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.
AUTHOR
Asiyeh
Nematizadeh
a.nematizadeh@yahoo.com
2
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.
LEAD_AUTHOR
[1] M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), pp. 181-188.
1
[2] S.S. Ali, J. Jain, and A. Rajput, A Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces, Int. J. Sci. Eng. Res., 4 (2013), pp. 1-6.
2
[3] J. Ali, M. Imdad, D. Mihet, and M. Tanveer, Common fixed points of strict contractions in Menger spaces, Acta Math. Hungar., 132 (2011), pp. 367-386.
3
[4] S.S. Chang, Y.J. Cho, and S.M. Kang, Nonlinear operator theory in probabilistic metric spaces, Nova Science Publishers Inc., New York, 2001.
4
[5] G. Deschrijver and E.E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets Syst., 133 (2003), pp. 227-235.
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[6] J.X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), pp. 1833-1843.
6
[7] J.X. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal., 70 (2009), pp. 184-193.
7
[8] M. Goudarzi, A generalized fixed point theorem in intuitionistic Menger spaces and its application to integral equations, Int. J. Math. Anal., 5 (2011), pp. 65-80.
8
[9] H.R. Goudarzi and M. Hatami Saeedabadi, On the definition of intuitionistic probabilistic 2-metric spaces and some results, J. Nonlinear Anal. Appl., (2014), pp. 1-8.
9
[10] O. Hadzic and E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets Syst., 127 (2002), pp. 333-344.
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[11] O. Hadzic, E. Pap, and M. Budincevic, A generalisation of tardiffs fixed point theorem in probabilistic metric spaces and applications to random equations, Fuzzy Sets Syst., 156 (2005), pp. 124-134.
11
[12] M. Imdad, J. Ali, and M. Hasan, Common fixed point theorems in modified intuitionistic fuzzy metric spaces, Iran. J. Fuzzy Syst., 5 (2012), pp. 77-92.
12
[13] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), pp. 771-779.
13
[14] I. Kubiaczyk and S. Sharma, Some common fixed point theorems in Menger space under strict contractive conditions, Southeast Asian Bull. Math., 32 (2008), pp. 117-124.
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[15] S. Kutukcu, A. Tuna, and A.T. Yakut, Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations, Appl. Math. & Mech., 28 (2007), pp. 799-809.
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[16] Y. Liu and Z. Li, Coincidence point theorem in probabilistic and fuzzy metric spaces, Fuzzy Sets Syst., 158 (2007), pp. 58-70.
16
[17] S. Manro and Sumitra, Common New Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces Using Implicit Relation, Appl. Math., 4 (2013), pp. 27-31.
17
[18] S. Manro, S.S. Bhatia, and S. Kumar, Common fixed point theorem for weakly compatible maps satisfying E.A. property in intuitionistic Menger space, J. Curr. Eng. & Maths, 1 (2012), pp. 5-8.
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[19] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA, 28 (1942), pp. 535-537.
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[20] D. Mihet, Multivalued generalisations of probabilistic contractions, J. Math. Anal. Appl., 304 (2005), pp. 464-472.
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[21] S.N. Mishra, Common fixed points of compatible mappings in PM-spaces, Math. Japonica, 36 (1991), pp. 283-289.
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[22] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), pp. 1039-1046.
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[23] B. Schweizer and A. Sklar, Probabilistic metric spaces, P. N. 275, North-Holland Seri. Prob. & Appl. Math., North-Holland Publ. Co. New York, 1983.
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[26] A. Sharma, A. Jain, and S. Choudhari, Sub-compatibility and fixed point theorem in intuitionistic Menger space, Int. J. Theor. & Appl. Sci., 3 (2011), pp. 9-12.
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[27] R. Shrivastava, A. Gupta, and R. N. Yadav, Common fixed point theorem in intuitionistic Menger space, Int. J. Math. Arch., 2 (2011), pp. 1622-1627.
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[28] B. Singh and S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl., 301 (2005), pp. 439-448.
28
[29] M. Tanveer, M. Imdad, D. Gopal, and D. Kumar Patel, Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.), Fixed Point Theory Appl., pp. 1-12.
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[30] S. Zhang, M. Goudarzi, R. Saadati, and S. M. Vaezpour, Intuitionistic Menger inner product spaces and applications to integral equations, Appl. Math. Mech. Engl. Ed., 31 (2010), pp. 415-424.
30
ORIGINAL_ARTICLE
The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points
In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.
https://scma.maragheh.ac.ir/article_34300_558e5017059030a2a631d70b10382c96.pdf
2019-02-01
51
65
10.22130/scma.2018.73451.302
Sturm-Liouville equation
Singular points
Turning points
Dual equations
Seyfollah
Mosazadeh
s.mosazadeh@kashanu.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran.
LEAD_AUTHOR
[1] V. Barcilon, Explicit solution of the inverse problem for a vibrating string, J. Math. Anal. Appl., 93 (1983), pp. 222-234.
1
[2] P.J. Browne and B.D. Sleeman, Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions, Inv. Prob., 12 (1996), pp. 377-381.
2
[3] A. Dabbaghian and Sh. Akbarpoor, The nodal points for uniqueness of inverse problem in boundary value problem with aftereffect, World Appl. Sci. J., 12 (2011), pp. 932-934.
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[4] G. Freiling and V.A. Yurko, Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter, Inv. Prob., 26 (2010), pp. 1-17.
4
[5] G. Freiling and V.A. Yurko, Inverse Sturm-Liouville problems and their applications, NOVA Science Publishers, New York, 2001.
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[6] I.M. Gelfand and B.M. Levitan, On the determination of a differential equation from its spectral function, Amer. Math. Soc. Transl. Ser. 2., 1 (1955), pp. 253-304.
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[7] O.H. Hald and J.R. Mclaughlin, Solution of inverse nodal problems, Inv. Prob., 5 (1989), pp. 307-347.
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[8] H. Kheiri, A. Jodayree Akbarfam, and A.B. Mingarelli, The uniqueness of the solution of dual equations of an inverse indefinite Sturm-Liouville problem, J. Math. Anal. Appl., 306 (2005), pp. 269-281.
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[9] H. Koyunbakan, The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition, Appl. Math. Lett., 18 (2010), pp.173-180.
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[10] V.A. Marchenko, Some problems in the theory of a second-order differential operator, Dokl. Akad. Nauk. SSSR., 72 (1950), pp. 457-460.
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[11] S. Mosazadeh, A new approach to uniqueness for inverse Sturm-Liouville problems on finite intervals, Turk. J. Math., 41 (2017), pp. 1224-1234.
11
[12] S. Mosazadeh, Infinite product representation of solution of indefinite Sturm-Liouville problem, Iranian J. Math. Chem., 4 (2013), pp. 27-40.
12
[13] A.S. Ozkan and B. Keskin, Spectral problems for Sturm-Liouville operators with boundary and jump conditions linearly dependent on the eigenparameter, Inv. Prob. Sci. Eng., 20 (2012), pp. 799-808.
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[14] J. Poschel and E. Trubowitz, Inverse Spectral Theory, Academic Press, London, 1987.
14
[15] W.A. Pranger, A formula for the mass density of a vibrating string in terms of the trace, J. Math. Anal. Appl., 141 (1989), pp. 399-404.
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[16] C.T. Shieh and V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl., 347 (2008), pp. 266-272.
16
[17] N. Topsakal, Inverse problem for Sturm-Liouville operators with Coulomb potential which have discontinuity conditions inside an interval, Math. Phys. Anal. Geom., 13 (2010), pp. 29-46.
17
[18] Y.P. Wang, A uniqueness theorem for Sturm-Liouville operators with eigenparameter dependent boundary conditions, Tamkang J. Math., 43 (2012), pp. 145-152.
18
[19] Y.P. Wang, Inverse problems for discontinuous Sturm-Liouville operators with mixed spectral data, Inv. Prob. Sci. Eng., 23 (2015), pp. 1180-1198.
19
[20] Y.P. Wang and V.A. Yurko, On the inverse nodal problems for discontinuous Sturm-Liouville operators, J. Diff. Equ., 260 (2016), pp. 4086-4109.
20
[21] C.F. Yang, Inverse nodal problems of discontinuous Sturm-Liouville operators, J. Diff. Equ., 254 (2013), pp. 1992-2014.
21
[22] V.A. Yurko, Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series, Utrecht: VSP, 2002.
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[23] V.A. Yurko, Inverse spectral problems for differential pencils on the half-line with turning points, J. Math. Anal. Appl., 320 (2006), pp. 439-463.
23
ORIGINAL_ARTICLE
Generalized Regular Fuzzy Irresolute Mappings and Their Applications
In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open and generalized regular fuzzy irresolute closed maps in fuzzy topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy irresolute maps are investigated. As a natural follow-up of the study of r-generalized regular fuzzy open sets, the concept of r-generalized regular fuzzy connectedness of a fuzzy set is introduced and studied.
https://scma.maragheh.ac.ir/article_32569_defba3886a0dcdce9088bd3affc8b0d8.pdf
2019-02-01
67
81
10.22130/scma.2018.57727.199
Generalized regular fuzzy irresolute
Generalized regular fuzzy irresolute open
Generalized regular fuzzy irresolute closed mapping
$r$-FRCO-$T_{1}$
$r$-FRCO-$T_{2}$
$r$-GRF-$T_{1}$
$r$-GRF-$T_{2}$
$r$-FRCO-regular
$r$-FRCO-normal
Strongly GRF-regular
strongly GRF-normal
$r$-GRF-separated sets
$r$-GRF-connectedness
Elangovan
Elavarasan
maths.aras@gmail.com
1
Department of Mathematics, Thiruvalluvar Arts and Science College (Affiliated to Thiruvalluvar University), Kurinjipadi, Tamil Nadu-607302, India.
LEAD_AUTHOR
[1] G. Balasubramanian and P. Sundaram, On some generalizations of fuzzy continuous functions, Fuzzy Set. Syst., 86 (1997), pp. 93-100.
1
[2] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182-190.
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[9] Y.C. Kim and J.M. Ko, $R$-generalized fuzzy closed sets, J. Fuzzy Math., 12 (2004), pp. 7-21.
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[11] T. Kubiak and A.P. Sostak, Lower set-valued fuzzy topologies, Quaest. Math., 20 (1997), pp. 423-429.
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[14] A.A. Ramadan, S.E. Abbas, and Y.C. Kim, Fuzzy irresolute mappings in smooth fuzzy topological spaces, J. Fuzzy Math., 9 (2001), pp. 865-877.
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[15] A.P. Sostak, Two decades of fuzzy topology: Basic ideas, Notion and results, Russian Math. Sur., 44 (1989), pp. 125-186.
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[16] A.P. Sostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II, 11 (1986), pp. 89-103.
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[18] A. Vadivel and E. Elavarasan, Applications of $r$-generalized regular fuzzy closed sets, Ann. Fuzzy Math. Infor., 12 (2016), pp. 719-738.
18
ORIGINAL_ARTICLE
Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces
Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C \rightarrow E $ be a nonlinear map, and let $u, v$ be positive numbers. In this paper, we show that the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for finding a unique solution of the variational inequality for $(u, v)$-cocoercive mappings in Banach spaces.
https://scma.maragheh.ac.ir/article_25887_4d361d95ff4721a03622269726d897e2.pdf
2019-02-01
83
92
10.22130/scma.2017.25887
Variational inequality
Nonexpansive mapping
$(u
v)$-cocoercive mapping
Metric projection
Sunny nonexpansive retraction
Ebrahim
Soori
sori.e@lu.ac.ir
1
Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran.
LEAD_AUTHOR
[1] R.P. Agarwal, D. Oregan, and D.R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, in: Topological Fixed Point Theory and its Applications, vol. 6, Springer, New York, 2009.
1
[2] R.E. Bruck, Nonexpansive projections on subsets of Banach spaces, Pacific. J. Math., 47 (1973), pp. 341-356.
2
[3] R.E. Bruck, Nonexpansive retract of Banach spaces, Bull. Amer. Math. Soc., 76 (1970), pp. 384-386.
3
[4] R.E. Bruck, Properties of fixed-point sets of nonexpansive mapping in Banach spaces, Trans. Amer. Math. Soc., 179 (1973), pp. 251-262.
4
[5] T. Ibarakia and W. Takahashi, A new projection and convergence theorems for the projections in Banach spaces, J. Approx. Theory , 149 (2007), pp. 1-14.
5
[6] S. Saeidi, Comments on relaxed $(gamma, r)$-cocoercive mappings, Int. J. Nonlinear Anal. Appl., 1 (2010), pp. 54-57.
6
[7] W. Takahashi, Convergence theorems for nonlinear projections in Banach spaces (in Japanese), RIMS Kokyuroku, 1396 (2004), pp. 49-59.
7
[8] W. Takahashi, Nonlinear Functional Analysis: Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, 2000.
8
ORIGINAL_ARTICLE
A class of new results in FLM algebras
In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.
https://scma.maragheh.ac.ir/article_28459_b7a5cf314e4ef6915c21f824caf64ba6.pdf
2019-02-01
93
100
10.22130/scma.2017.28459
Fundamental topological algebra
FLM algebra
Spectrum
Multiplicative linear functional
Ali
Naziri-Kordkandi
ali_naziri@pnu.ac.ir
1
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
LEAD_AUTHOR
Ali
Zohri
zohri_a@pnu.ac.ir
2
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
AUTHOR
Fariba
Ershad
fershad@pnu.ac.ir
3
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
AUTHOR
Bahman
Yousefi
b_yousefi@pnu.ac.ir
4
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
AUTHOR
[1] E. Ansari-Piri, A class of factorable topological algebras, Proc. Edin. Math. Soc., 33 (1990), pp. 53-59.
1
[2] E. Ansari-Piri, Topics on fundamental topological algebras, Honam math. J., 23 (2001), pp. 59-66.
2
[3] E. Ansari-Piri, The linear functionals on fundamental locally multiplicative topological algebras, Turk. J. Math., 33 (2010), pp. 385-391.
3
[4] F.F. Bonsal and J. Doncan, Complete normed algebras, Springer-Verlag, Berlin 1937.
4
[5] H.G. Dales, Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.
5
[6] M. Fragoulopoulou, Topological algebras with involution, Elsevier, 2005.
6
[7] S. Kowalski and Z. Slodkowaski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math, 67 (1980), pp. 215-223.
7
[8] W. Rudin, Functional analysis, McGraw- Hill, 1973.
8
[9] A. Zohri and A. Jabbari, Generalization of some properties of Banach algebras to fundamental locally multiplicative topological algebras, Turk J Math, 35 (2011), pp. 1-7.
9
ORIGINAL_ARTICLE
Observational Modeling of the Kolmogorov-Sinai Entropy
In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ \Theta $. The relative entropy of a sub-$ \sigma_\Theta $-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical systems are investigated. Also, a relative version of Kolmogorov-Sinai theorem is given. Finally, it is proved that the relative entropy of a relative $ \Theta $-measure preserving transformations with respect to a relative sub-$\sigma_\Theta$-algebra having finite atoms is affine.
https://scma.maragheh.ac.ir/article_29983_7a5face43ae162c0c5d62beecf8dc888.pdf
2019-02-01
101
114
10.22130/scma.2018.29983
Relative entropy
Relative semi-dynamical system
$m_Theta$-equivalence
$m_Theta$-generator
$ (Theta_1
Theta_2) $-isomorphism
Uosef
Mohammadi
u.mohamadi@ujiroft.ac.ir
1
Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.
LEAD_AUTHOR
[1] M. Ebrahimi and U. Mohammadi, m-Generators of fuzzy dynamical systems, Cankaya. Univ. J. Sci. Eng., 9 (2012), pp. 167-182.
1
[2] U. Mohammadi, Relative information functional of relative dynamical systems, J. Mahani. Mat. Res. Cent., 2 (2013), pp. 17-28.
2
[3] U. Mohammadi, Weighted information function of dynamical systems, J. Math. Comput. Sci., 10 (2014), pp. 72-77.
3
[4] U. Mohammadi, Weighted entropy function as an extension of the Kolmogorov-Sinai entropy, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 4 (2015), pp. 117-122.
4
[5] U. Mohammadi, Relative entropy functional of relative dynamical systems, Cankaya. Univ. J. Sci. Eng., 2 (2014), pp. 29-38.
5
[6] M.R. Molaei, Relative semi-dynamical systems, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 12 (2004), pp. 237-243.
6
[7] M.R. Molaei, Mathematical modeling of observer in physical systems, J. Dyn. Syst. Geom. Theor., 4 (2006), pp. 183-186.
7
[8] M.R. Molaei, Observational modeling of topological spaces, Chaos Solitons Fractals, 42 (2009), pp. 615-619.
8
[9] M.R. Molaei, M.H. Anvari, and T. Haqiri, On relative semi-dynamical systems, Intell. Autom. Soft Comput. Syst., 12 (2004), pp. 237-243.
9
[10] M.R. Molaei and B. Ghazanfari, Relative entropy of relative measure preserving maps with constant observers, J. Dyn. Syst. Geom. Theor., 5 (2007), pp. 179-191.
10
[11] Ya. Sinai, On the notion of entropy of a dynamical system, Dokl. Akad. Nauk. S.S.S.R, 125 (1959), pp. 768-771.
11
[12] P. Walters, An Introduction to Ergodic Theory, Springer Verlag, 1982.
12
ORIGINAL_ARTICLE
A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence
In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $\frac{1+\sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore, new sequences have been used in order to introduce a new class of series. All properties of the sequences and related series are illustrated in the work by providing the details including sequences formula, related theorems, proofs and convergence analysis of the series.
https://scma.maragheh.ac.ir/article_34323_062ea721f5f1adbe65dd5025387cba8d.pdf
2019-02-01
115
127
10.22130/scma.2018.62087.231
Fibonacci numbers
Golden Ratio
Convergence analysis
Moosa
Ebadi
moosa.ebadi@yahoo.com
1
Department of Mathematics, University of Farhangian, Tehran, Iran.
LEAD_AUTHOR
Farnaz
Soltanpour
soltanpoor.farnaz@yahoo.com
2
Department of Mathematics, University of Farhangian, Tehran, Iran.
AUTHOR
[1] I. Babolian, Topics in discrete mathematics, Mobtakeran publisher, Tehran, 1996.
1
[2] M. Ebadi and I.M. Maleki, Learning mathematics based on algorithms, Nashreolum publisher, 2014.
2
[3] J. Stoer and R. Bulirsch, Introduction to numerical analysis, Second edition, Springer, 1992.
3
[4] H.S. Kim and J. Neggers, Fibonacci mean and golden section mean, Computers and mathematics with applications, 56 (2008), pp. 228-232.
4
[5] M. Startek, A. Wloch, and I. Wloch, Fibonacci numbers and Lucas numbers in graphs, Discrete applied mathematics, 157 (2009), pp. 864-868.
5
ORIGINAL_ARTICLE
Richardson and Chebyshev Iterative Methods by Using G-frames
In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:H\rightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern, Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper, these schemes exploit the almost recently developed notion of g-frames which result in modified convergence rates compared with early computed ones in corresponding classical formulations. In fact, these convergence rates are formed by the lower and upper bounds of the given g-frame. Therefore, we can determine any convergence rate by considering an appropriate g-frame.
https://scma.maragheh.ac.ir/article_31814_ef793a9c97fed9f9c9716480c9dad7d0.pdf
2019-02-01
129
139
10.22130/scma.2018.68917.266
Hilbert space
$g$-frame
Operator equation
Iterative method
Chebyshev polynomials
Hassan
Jamali
jamali@vru.ac.ir
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
LEAD_AUTHOR
Mohsen
Kolahdouz
mkolahdouz@post.vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AUTHOR
[1] A. Askari Hemmat and H. Jamali, Adaptive Galerkin frame methods for solving operator equation, U.P.B. Sci. Bull., Series A, 73 (2011), pp. 129-138.
1
[2] K. Atkinson, W. Han, Theoretical Numerical Analysis, Springer, Third edition, 2009.
2
[3] D. Braess, Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory, Cambridge, Third edition, 2007.
3
[4] C.C. Cheny, Introduction to Approximation Theory, McGraw Hill, New York, 1966.
4
[5] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.
5
[6] S. Dahlke, M. Fornasier, and T. Raasch, Adaptive frame methods for elliptic operator equations, Advances in comp. Math., 27 (2007), pp. 27-63.
6
[7] H. Jamali and S. Ghaedi, Applications of frames of subspaces in Richardson and Chebyshev methods for solving operator equations, Math. Commun., 22 (2017), pp. 13-23 .
7
[8] H. Jamali and N. Momeni, Application of g-frames in conjugate gradient, Adv. Pure Appl. Math., 7 (2016), pp. 205-212.
8
[9] A. Najati, M. H. Faroughi, and A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Funct. Anal. Topology, 14 (2008), pp. 271-286.
9
[10] Y. Saad, Iterative methods for Sparse Linear Systems, PWS press, New York, 2000.
10
[11] R. Stevenson, Adaptive solution of operator equations using wawelet frames, SIAM J. Numer. Anal., 41 (2003), pp. 1074-1100.
11
[12] W. Sun, G-frames and G-Riesz Bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
12
[13] W. Sun, Stability of g-frames, J. Math. Anal. Appl., 326 (2007), pp. 858-868.
13
ORIGINAL_ARTICLE
Some Fixed Point Results on Intuitionistic Fuzzy Metric Spaces with a Graph
In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, we present some iterative scheme results for $G$-fuzzy contractive and $G$-fuzzy nonexpansive mappings on graphs.
https://scma.maragheh.ac.ir/article_29018_3207b7fee935ce78fea9497d8eb53f58.pdf
2019-02-01
141
152
10.22130/scma.2017.29018
Fixed point
Intuitionistice fuzzy metric space
Connected graph
$G$-fuzzy contractive
$G$-fuzzy nonexpansive
Mohammad Esmael
Samei
me_samei@yahoo.com
1
Department of Mathematics, Faculty of Science, University of Bu-Ali Sina, P.O.Box 6517838695, Hamedan, Iiran.
LEAD_AUTHOR
[1] R.P. Agarwal, M.A. El-Gebeily, and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Analysis, 87 (2008), pp. 109-116.
1
[2] C. Alaca, D. Turkoghlu, and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 29 (2006), pp. 1073-1078.
2
[3] S.M.A. Aleomraninejad, Sh. Rezapour, and N. Shahzad, Some fixed point results on metric space witha graph, Topology Appl., 159 (2012), pp. 659-663.
3
[4] I. Altun and G. Durmaz, Some fixed point results in cone metric spaces, Rend Circ. Math. Palermo, 58 (2009), pp. 319-325.
4
[5] K. Atanassov, Intuitionistic fuzzy Sets, Fuzzy Sets and Systems, 20 (1986), pp. 87-96.
5
[6] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), pp. 133-181.
6
[7] I. Beg, A.R. Butt, and S. Radojevic, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60 (2010), pp. 1214-1219.
7
[8] V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Analysis, 74 (2011), pp. 7347-7355.
8
[9] J. Caristi, Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), pp. 241-251.
9
[10] D. Coker, An introduction to intuitionistic fuzzy metric spaces, Fuzzy Sets and Systems, 88 (1997), pp. 81-89.
10
[11] C. Di Bari and, C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend Circ. Math. Palermo, 52 (2003), pp. 315-321.
11
[12] F. Echenique, A short and constructive proof of Tarski's fixed point theorem, Internat, J. Game Theory, 33(2) (2005), pp. 215-218.
12
[13] M.S. El Naschie, A review of E-infinity theory and the mass spectrum of high energy particle physics, Chaos, solitons and Fractals, 19 (2004), pp. 209-236.
13
[14] M.S. El Naschie, On a fuzzy Kahler-like manifold which is consistent with two-slit experiment, Int. J. Nonlinear Science and Numerical Simul., 6 (2005), pp. 95-98.
14
[15] M.S. El Naschie, On the uncertainty of Contorian geometry and two-slit experiment, Chaos, Soliton and Fractals, 9 (1998), pp. 517-529.
15
[16] M.S. El Naschie, On the verification of heterotic strings theory and ε(∞) theory, Chaos, Soliton and Fractals, 11 (2000), pp. 2397-2407.
16
[17] M.S. El Naschie, On two new fuzzy Kahler manifolds, Klein modular space and Hooft holographic principles, Chaos, Solitons and Fractals, 29 (2006), pp. 876-881.
17
[18] M.S. El Naschie, The idealized quantum two-slit Gedanken experiment revisited criticism and reinterpretation, Chaos, Solitons and Fractals, 27 (2006), pp. 843-849.
18
[19] R. Espinola and W.A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153 (2006), pp. 1046-1055.
19
[20] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), pp. 385-389.
20
[21] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), pp. 395-399.
21
[22] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), pp. 245-252.
22
[23] G. Gwozdz-Lukawska and J. Jachymski, IFS on metric space with a graph structure and extentions of the Kelisky-Rivilin theorem, J. Math. Anal. Appl., 356 (2009), pp. 453-463.
23
[24] T.L. Hicks, Fixed point theorems for quasi-metric spaces, Math. Japon., 33 (1988), pp. 231-236.
24
[25] J. Jachymski, The contraction principle for mappings on metric space with a graph, Proc, Amer. Math. Soc., 136 (2008), pp. 1359-1373.
25
[26] S.G. Jeong and B.E. Rhoades, More maps for which F(T)=F(Tn), Demonestraio Math., 40 (2007), pp. 671-680.
26
[27] H. Karayilan and M. Telci, Common fixed point theorem for contractive type mappings in fuzzy metric spaces, Rend. Circ. Mat. Palermo., 60 (2011), pp. 145-152.
27
[28] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), pp. 326-334.
28
[29] K. Menger, Statistical metrices, Proc. Natl. Acad. Sci., 28 (1942), pp. 535-537.
29
[30] D. Mihet, A banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), pp. 431-439.
30
[31] J.H. Park, Intiutionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), pp. 1039-1046.
31
[32] J.S. Park, Y.C. Kwun, and J.H. Park, A fixed point theorem in the intiutionistic fuzzy metric spaces, Far East J. Math. Sci., 16 (2005), pp. 137-149.
32
[33] M. Rafi and M.S.M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces, Iranian J. of Fuzzy Systems, 3 (2006), pp. 23-29.
33
[34] Sh. Rezapour and P. Amiri, Some fixed point results for multivalued operators in generalized metric spaces, Computers and Mathematics with Applications, 61 (2011), pp. 2661-2666.
34
[35] Sh. Rezapour and R. Hamlbarani, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Analysis Appl., 345 (2008), pp. 719-724.
35
[36] J. Rodriquez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), pp. 173-176.
36
[37] B. Samet, C. Vetro, and P. Vetro, Fixed point theorem for α-ψ-contractive type mappings, Nonlinear Analysis, 75 (2012), pp. 2154-2165.
37
[38] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), pp. 314-334.
38
[39] L.D.J. Sigalotte and A. Mejias, On El Naschie's conjugate complex time, fractal E(∞) space-time and faster-than-light particles, Int. J. Nonlinear Sci. Number Simul., 7 (2006), pp. 467-472.
39
[40] P. Veeramani, Best approximation in fuzzy metricspaces, Journal of fuzzy mathematics, 9 (2001), pp. 75-80.
40
[41] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), pp. 338-353.
41
ORIGINAL_ARTICLE
On Approximate Birkhoff-James Orthogonality and Approximate $\ast$-orthogonality in $C^\ast$-algebras
We offer a new definition of $\varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $\varepsilon$-orthogonality in an arbitrary $C^\ast$-algebra $\mathcal{A}$, as a Hilbert $C^\ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.
https://scma.maragheh.ac.ir/article_30861_f0543a2f5639a20e512cc2c244fb4bd2.pdf
2019-02-01
153
163
10.22130/scma.2018.62262.233
Approximate orthogonality
Birkhoff--James orthogonality
Range-kernel orthogonality
$C^ast$-algebra
$ast$-orthogonality
Seyed Mohammad Sadegh
Nabavi Sales
sadegh.nabavi@gmail.com
1
Department of Mathematics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
LEAD_AUTHOR
[1] J. Anderson, On normal derivations, Proc. Amer. Math. Soc, 38 (1973), pp. 135-140.
1
[2] L. Arambasic and R. Rajic, A strong version of the Birkhoff-James orthogonality in Hilbert C*-modules, Ann. Funct. Anal., 5 (2012), pp. 109-120.
2
[3] L. Arambasic and R. Rajic, The Birkhoff-James orthogonality in Hilbert C*-modules, Linear Algebra Appl., 437 (2012), pp. 1913-1929.
3
[4] G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J., 1 (1935), pp. 169-172.
4
[5] A. Blanco and A. Turnsek, On the converse of Anderson's theorem, Linear Alg ebra Appl., 424 (2007),pp. 384-389.
5
[6] J. Chmielinski, On an ε-Birkhoff orthogonality, J. Inequal. Pure Appl. Math., 6 (2005), Art. 79.
6
[7] S.S. Dragomir, On approximation of continuous linear functionalsin normed linear spaces, An. Univ. Timisoara Ser. Stiint. Mat., 29 (1991), pp. 51-58.
7
[8] S.S. Dragomir, Semi-Inner Products and Applications, Nova Science Publishers, Inc., Hauppauge, NY, 2004.
8
[9] P.B. Duggal, Range kernel orthogonality of derivations, Linear Algebra appl., 304 (2000), pp. 103-108.
9
[10] D. Ilisevic and A. Turnsek, Approximately orthogonality preserving mappings on C*-modules, J. Math. Anal. Appl., 341 (2008), pp. 298-308.
10
[11] R.C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 61 (1947), pp. 265-292.
11
[12] D. Keckic, Orthogonality of the range and the kernel of some elementary operators, Proc. Amer. Math. Soc., 128 (2000), pp. 3369-3377.
12
[13] E.C. Lance, Hilbert C*-modules. A Toolkitfor Operator Algebraists, London Mathematical Society Lecture Note Series vol. 210, Cambridge University Press, Cambridge, 1995.
13
[14] S. Mecheri, Non-normal derivations and orthogonality, Proc. Amer. Math. Soc. 133 (2004), no 3, 759-762.
14
[15] M.S. Moslehian and S.M.S. Nabavi Sales, Fuglede-Putnam type theorems via the Aluthge transform, Positivity, 17 (2013), pp. 151-162.
15
[16] A. Turnv sek, Generalized Anderson's inequality, J. Math. Anal. Appl., 263 (2001), pp. 121-134.
16
ORIGINAL_ARTICLE
Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. We obtain a $*$-frame by an orthogonal projection and a given $*$-frame, characterize its duals, and give a bilateral condition for commutating frame operator of a primary $*$-frame and an orthogonal projection. At the end of paper, pre-frame operator of a dual frame is computed by pre-frame operator of a general $*$-frame and an orthogonal projection.
https://scma.maragheh.ac.ir/article_34304_f1fa1d7d30cfa5a319737d9fba040b79.pdf
2019-02-01
165
177
10.22130/scma.2018.59232.206
Dual frame
Equivalent $*$-frame
Frame operator
$*$-frame
Operator dual frame
Azadeh
Alijani
a.alijani57@gmail.com
1
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.
LEAD_AUTHOR
[1] A. Alijani, Dilations of $*$-frames and their operator duals, Under Review.
1
[2] A. Alijani and M.A. Dehghan, $*$-Frames in Hilbert $C^*$-modules, U.P.B. Sci. Bull., Series A, 73 (2011), pp. 89-106.
2
[3] P.G. Casazza, The art of frame theory, Taiw. J. Math., 4 (2000), pp. 129-201.
3
[5] M.A. Dehghan and M.A. Hasankhani Fard, G-Dual frames in Hilbert spaces, U.P.B. Sci. Bull., Series A, 75 (2013), pp. 129-140.
4
[6] M. Frank and D.R. Larson, Frames in Hilbert $C^*$-modules and $C^*$-algebra, J. Operator theory, 48 (2002), pp. 273-314.
5
[7] E.C. Lance, Hilbert $C^*$-modules, A Toolkit for Operator Algebraists, University of Leeds, Cambridge University Press, 1995.
6
ORIGINAL_ARTICLE
Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces
In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, \textit{e.g.}, in [21] and [22]. In the last section of the paper, we define the notion of almost generalized $(\psi ,\varphi )_{s,a}$-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciric et.al. in [23] to the setting of $b_{2}$-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature.
https://scma.maragheh.ac.ir/article_29263_f6da7913f6ba4c54cf195c5e7a308a31.pdf
2019-02-01
179
212
10.22130/scma.2017.29263
Fixed point
Complete metric space
Ordered $b_2$-metric space
Roghaye
Jalal Shahkoohi
rog.jalal@gmail.com
1
Department of Mathematics, Aliabad katoul Branch, Islamic Azad University, Aliabad katoul, Iran.
AUTHOR
Zohreh
Bagheri
zohrehbagheri@yahoo.com
2
Department of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran.
LEAD_AUTHOR
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28
ORIGINAL_ARTICLE
Surjective Real-Linear Uniform Isometries Between Complex Function Algebras
In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A \longrightarrow B$, where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${\rm ER}\left (A, X\right ) = {\rm Ch}\left (A, X\right )$ and ${\rm ER}\left (B, Y\right ) = {\rm Ch}\left (B, Y\right )$. Next, we give a description of $ T $ whenever $ A $ and $ B $ are complex function algebras and $ T $ does not assume to be unit-preserving.
https://scma.maragheh.ac.ir/article_30145_1313cd222b3fef5233599be64c52c1b4.pdf
2019-02-01
213
240
10.22130/scma.2018.30145
Choquet boundary
Function algebra
Function space
Real-linear uniform isometry
Hadis
Pazandeh
pazandeh63@gmail.com
1
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.
AUTHOR
Davood
Alimohammadi
alimohammadi.davood@gmail.com
2
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.
LEAD_AUTHOR
[1] D. Alimohammadi and T. Ghasemi Honary, Choquet and Shilov boundaries, peak sets and peak points for real Banach function algebras, Journal of Function Spaces and Applications, 2013 (2013), pp. 1-9.
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[4] A. Jamshidi and F. Sady, Real-linear isometries between certain subspaces of continuous functions, Cent. Eur. J. Math., 11 (2013), pp. 2034-2043.
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[5] E. Kaniuth, A Course in Commutative Banach Algebras, Springer, 2009.
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[8] T. Miura, Real-linear isometries between function algebras, Cent. Eur. J. Math., 9 (2011), pp. 778-788.
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9