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Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance

Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance Combining certain existing concepts we define a new multi-valued contraction with respect to w-distance. The underline metric space is assumed to have a relation defined on it. We prove the existence of non-null fixed point sets for these mappings under appropriate assumptions. The uniqueness of the fixed point is proved separately under some additional conditions. We also discuss Hyers–Ulam–Rassias stability and well-posedness property of the fixed point problem. For that purpose we formulate them here in terms of w-distance. There are several corollaries, illustrative examples and remarks. Some existing results are shown to be extended by our result. The study is in the domain of multi-valued relational fixed point theory with w-distance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Fixed point problem of a multi-valued Kannan–Geraghty type contraction via w-distance

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References (40)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to The Forum D’Analystes 2022
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-022-00457-3
Publisher site
See Article on Publisher Site

Abstract

Combining certain existing concepts we define a new multi-valued contraction with respect to w-distance. The underline metric space is assumed to have a relation defined on it. We prove the existence of non-null fixed point sets for these mappings under appropriate assumptions. The uniqueness of the fixed point is proved separately under some additional conditions. We also discuss Hyers–Ulam–Rassias stability and well-posedness property of the fixed point problem. For that purpose we formulate them here in terms of w-distance. There are several corollaries, illustrative examples and remarks. Some existing results are shown to be extended by our result. The study is in the domain of multi-valued relational fixed point theory with w-distance.

Journal

The Journal of Analysis – Springer Journals

Published: Mar 1, 2023

Keywords: w-distance; Kannan contraction; Geraghty type mapping; Hyers–Ulam–Rassias stability; Well-posedness; 47H10; 54H25

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