Document Type: Special Issue on Fixed Point Theory
Author
Department of Mathematics, Ordu University, Altinordu 52200 Ordu, Turkey
Abstract
In this work, we prove some fixed point theorems by using $wt$-distance on b-metric spaces. Our results generalize some fixed point theorems in the literature. Moreover, we introduce $wt_0$-distance and by using the concept of $wt_0$-distance, we obtain some coupled fixed point results in complete b-metric spaces.
Keywords
Main Subjects
[1] A. A. N. Abdou, Y. J. Cho, R. Saadeti, Distance type and common fixed point theorems in Menger probabilistic metric type spaces, Appl. Math. Comput. 265 (2015), 1145-1154.
[2] P. Amiri, Sh. Rezapour, N. Shahzad, Fixed points of generalized α-ψ-contractions, RACSAM. 108 (2) (2014), 519-526.
[3] JH. Asl, S. Rezapour, N. Shahzad, On fixed points of (α-ψ)-contractive multifunctions, Fixed Point Theory Appl. (2012), 2012:212.
[4] Z. Badehian, M. S. Asgari, Fixed point theorems for α-ψ-ϕ-contractive integral type mappings, J. Linear. Topological. Algebra. 3 (4) (2014), 219-230.
[5] V. Berinde, Generalized contractions in quasimetric spaces, “Babes-Bolyai” University-Preprint Seminar on Fixed Point Theory, 93 (3) (1993), 3-9.
[6] V. Berinde, Sequences of operators and fixed points in quasi-metric spaces, Mathematica. 41 (4) (1996), 23-27.
[7] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393.
[8] M. F. Bota, E. Karapinar, O. Mle¸ snit ¸e, Ulam-Hyers stability results for fixed point problems via α-ψ-contractive mapping in b-metric space, Abstr. Appl. Anal. (2013), 2013:825293.
[9] M. F. Bota, C. Chifu, E. Karapinar, Fixed point theorems for generalized (α∗-ψ)-Ciric-type contractive multivalued operators in b-metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 1165-1177.
[10] S. H. Cho, Fixed points for multivalued mappings in b-metric spaces, Appl. Math. Sci. 10 (59) (2016), 2927-2944.
[11] S. Czerwik, Contraction mappings in b-metric spaces, Acta. Math. et Infor. Uni. Ostraviensis. 1 (1993), 5-11.
[12] M. Demma, R. Sadaati, P. Vetro, Multi-valued operators with respect wt-distance on metric type spaces, Bull. Iranian Math. Soc. 42 (6) (2016), 1571-1582.
[13] N. Hussain, R. Saadati, R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory and Appl. (2014), 2014:88.
[14] O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Sci. Math. Jpn. 44 (2) (1996), 381-391.
[15] W. A. Kirk, N. Shahzad, Fixed point theory in Distance Spaces, Springer-Heidelberg, 2014.
[16] A. Kostic, V. Rakocevic, S. Radenovic, Best proximity points involving simulation functions with w0-distance, RACSAM (2018), in press.
[17] H. Lakzian, D. Gopal, W. Sintunavarat, New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations, J. Fixed Point Theory Appl. 18 (2016), 251-266.
[18] A. Mbarki, R. Oubrahim, Probabilistic b-metric spaces and nonlinear contractions, Fixed Point Theory Appl. (2017), 2017:29.
[19] R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (3) (2017), 2153-2163.
[20] S. K. Mohanta, Some fixed point theorems using wt-distance in b-metric spaces, Fasc. Math. 54 (2015), 125-140.
[21] S. K. Mohanta, S. Patra, Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph, J. Linear. Topological. Algebra. 6 (4) (2017), 301-321.
[22] C. Mongkolkeha, Y. J. Cho, P. Kumam, Fixed point theorems for simulation functions in b-metric spaces via the wt-distance, Appl. Gen. Topol. 18 (1) (2017), 91-105.
[23] S. Nadaban, Fuzzy b-Metric Spaces, Int. J. Comput. Commun. Control. 11 (2) (2016), 273-281.
[24] J. J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order. 22 (2005), 223-239.
[25] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and applications to matrix equations, Proc. Amer. Math. Soc. 132 (2003), 1435-1443.
[26] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α−ψ-contractive type mappings, Nonlinear Anal. 75 (2012), 2154-2165.
[27] B. Samet, The class of (α − ψ)-type contractions in b-metric spaces and fixed point theorems, Fixed Point Theory Appl. (2015), 2015:1.
[28] R. J. Shahkoohi, A. Razani, Fixed Point Theorems for semi λ-subadmissible Contractions in b-Metric spaces, J. Linear. Topological. Algebra. 3 (4) (2014), 219-230.
[29] X. Wu, Generalized α-ψ contractive mappings in partial b-metric spaces and related fixed point theorems, J. Nonlinear Sci. Appl. 9 (2016), 3255-3278.
