Fixed point theorems by combining Jleli and Samets, and Branciaris inequalities
Antonio Francisco Roldán López de Hierroa
- Department of Quantitative Methods for Economics and Business, University of Granada, Granada, Spain.
- PAIDI Research Group FQM-268, University of Jaén, Jaén, Spain.
- Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia.
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.
- Generalized metric space
- Branciari metric space
- fixed point
- contractive mapping.
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