Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities


Authors

Antonio Francisco Roldan Lopez de Hierroa - Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain. - PAIDI Research Group FQM-268, University of Jaen, Jaen, Spain. Naseer Shahzad - Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia.


Abstract

The aim of this paper is to introduce a new class of generalized metric spaces (called RS-spaces) that unify and extend, at the same time, Branciari’s generalized metric spaces and Jleli and Samet’s generalized metric spaces. Both families of spaces seen to be different in nature: on the one hand, Branciari’s spaces are endowed with a rectangular inequality and their metrics are finite valued, but they can contain convergent sequences with two different limits, or convergent sequences that are not Cauchy; on the other hand, in Jleli and Samet’s spaces, although the limit of a convergent sequence is unique, they are not endowed with a triangular inequality and we can found two points at infinite distance. However, we overcome such drawbacks and we illustrate that many abstract metric spaces (like dislocated metric spaces, b-metric spaces, rectangular metric spaces, modular metric spaces, among others) can be seen as particular cases of RS-spaces. In order to show its great applicability, we present some fixed point theorems in the setting of RS-spaces that extend well-known results in this line of research.


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ISRP Style

Antonio Francisco Roldan Lopez de Hierroa, Naseer Shahzad, Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3822--3849

AMA Style

Lopez de Hierroa Antonio Francisco Roldan, Shahzad Naseer, Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities. J. Nonlinear Sci. Appl. (2016); 9(6):3822--3849

Chicago/Turabian Style

Lopez de Hierroa, Antonio Francisco Roldan, Shahzad, Naseer. "Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3822--3849


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