Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces

Binayak S. Choudhury; Nikhilesh Metiya; Sunirmal Kundu; Debashis Khatua

doi:10.2478/amsil-2022-0020

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Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 1 (March 2023)

By: Binayak S. Choudhury, Nikhilesh Metiya , Sunirmal Kundu and Debashis Khatua

Open Access

|Dec 2022

Abstract

In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0020 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 32 - 48

Submitted on: Oct 19, 2021

Accepted on: Nov 23, 2022

Published on: Dec 20, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

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© 2022 Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Debashis Khatua, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 37 (2023): Issue 1 (March 2023)