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Optimal Common Fixed Point Results in Complete Metric Spaces with w-distance

Document Type : Research Paper

Author

Department of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395-3697, Tehran, Iran.

Abstract

In this article, we will study the existence and uniqueness of optimal common fixed points for self-mappings in metric spaces with w-distance. We obtain generalizations of the Kocev and Rako\v{c}evi'{c} fixed point theorems. The obtained results do not require the continuity or the condition $(C;k)$ of maps,  but require the weaker condition $(W)$. We also improve some of our results when the metric space is equipped with a w$_0$-distance. In this way, we get new existence results for non-cyclic quasi-contraction mappings of the Fisher type.

Keywords

References
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Sahand Communications in Mathematical Analysis
Volume 19, Issue 4
October 2022
Pages 117-132
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