# Existence, data dependence and stability of fixed points of multivalued maps in incomplete metric spaces

### 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.

### Keywords

metric space; α-completeness; α-continuity; fixed point; data dependence; stability

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*Annales Mathematicae Silesianae*,

*37*(1), 32-48. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/14987

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur India

Department of Mathematics, Sovarani Memorial College, Jagatballavpur India

https://orcid.org/0000-0002-6579-7204

Department of Mathematics, Government General Degree College, Salboni India

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur India

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