Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities
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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.
Share and Cite
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
Keywords
- Generalized metric space
- Branciari metric space
- fixed point
- contractive mapping.
MSC
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