Meir-Keeler theorem in b-rectangular metric spaces
-
2334
Downloads
-
3989
Views
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].
Share and Cite
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
References
-
[1]
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, (1980), 26–37.
-
[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.
-
[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.
-
[14]
T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317.
-
[15]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.