Existence and data dependence results for the fixed points of multivalued mappings

TL;DR

This paper introduces new classes of multivalued mappings and establishes fixed point existence and data dependence results for these mappings, expanding the theoretical framework for multivalued fixed point theory.

Contribution

It presents novel multivalued enriched contractive mappings and proves fixed point existence and data dependence results for these classes, advancing the theoretical understanding.

Findings

Existence of fixed points for new multivalued mappings.

Data dependence results for fixed points.

Extension of fixed point theory to enriched multivalued mappings.

Abstract

We introduce multivalued G\'{o}rnicki mapping and various new types of multivalued enriched contractive mappings, viz., multivalued enriched Kannan mapping, multivalued enriched Chatterjea mapping, and multivalued enriched Ciri\'{c}-Reich-Rus mapping. Then we establish some existence results for the fixed points of these multivalued contractive type mappings using the fixed point property of the average operator of the mappings. Furthermore, we present some data dependence results for the fixed points of mentioned classes of mappings.