<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Published Online: Dec 20, 2022

Page range: 32 - 48

Received: Oct 19, 2021

Accepted: Nov 23, 2022

DOI: https://doi.org/10.2478/amsil-2022-0020

Keywords
metric space, α-completeness, α-continuity, fixed point, data dependence, stability

© 2023 Binayak S. Choudhury et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Dec 20, 2022

Page range: 32 - 48

Received: Oct 19, 2021

Accepted: Nov 23, 2022

DOI: https://doi.org/10.2478/amsil-2022-0020

Keywordsmetric space, α-completeness, α-continuity, fixed point, data dependence, stability

© 2023 Binayak S. Choudhury et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
metric space, α-completeness, α-continuity, fixed point, data dependence, stability