Meir-Keeler theorem in b-rectangular metric spaces

Volume 10, Issue 4, pp 1786--1790 http://dx.doi.org/10.22436/jnsa.010.04.39

Publication Date: April 20, 2017 Submission Date: July 20, 2016

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Authors

Dingwei Zheng - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China. Pei Wang - School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi 537000, P. R. China. Nada Citakovic - Milirtary Academy, Generala Pavla, Jurisica Sturma 33, 11000 Belgrade, Serbia.

Abstract

In this paper, we prove a Meir-Keeler theorem in b-rectangular metric spaces. Thus, we answer the open question raised by Ding et al. [H. S. Ding, V. Ozturk, S. Radenović, J. Nonlinear Sci. Appl., 8 (2015), 378–386].

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ISRP Style

Dingwei Zheng, Pei Wang, Nada Citakovic, Meir-Keeler theorem in b-rectangular metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1786--1790

AMA Style

Zheng Dingwei, Wang Pei, Citakovic Nada, Meir-Keeler theorem in b-rectangular metric spaces. J. Nonlinear Sci. Appl. (2017); 10(4):1786--1790

Chicago/Turabian Style

Zheng, Dingwei, Wang, Pei, Citakovic, Nada. "Meir-Keeler theorem in b-rectangular metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1786--1790

Keywords

Fixed point
b-metric space
rectangular metric space
b-rectangular metric space.

MSC

47H10
54H25

References

[1] I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, (1980), 26–37.
- MathSciNet
- Google Scholar

[2] F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895–3901.

[3] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31–37.

[4] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11.
- Google Scholar

[5] H.-S. Ding, M. Imdad, S. Radenović, J. Vujaković, On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab J. Math. Sci., 22 (2016), 151–164.

[6] H.-S. Ding, V. Ozturk, S. Radenović, On some new fixed point results in b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 378–386.

[7] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages.

[8] H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 11 pages.

[9] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257– 290.

[10] A. F. Roldán López de Hierro, N. Shahzad, New fixed point theorem under R-contractions, Fixed Point Theoery Appl., 2015 (2015), 18 pages.

[11] B. Samet, Discussion on: a fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces by A. Branciari, Publ. Math. Debrecen, 76 (2010), 493–494.

[12] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\) -contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165

[13] I. R. Sarma, J. M. Rao, S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 180–182.
- Google Scholar

[14] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317.
- View Article
- Google Scholar

[15] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.