Generalizations of Certain Classes of Single-Valued Mappings to Multivalued Cases
Emirhan Hacioğlu
TL;DR
The paper addresses extending fixed-point results to multivalued mappings on metric spaces for several contractive-type classes. It develops a unified framework that subsumes perimeter-contracting, total-pairwise-distance, and generalized orbital triangular contractions, and proves fixed-point results (often under the absence of 2-periodic points) using Picard-type iterations. Key contributions include multivalued generalizations of perimeter-contracting, total-distance, and orbital triangular contractions in Kannan and Chatterjea variants, along with structural results connecting periodic points to fixed points. The work broadens classical fixed-point theory to multivalued settings, enhancing applicability to analysis and optimization in spaces of sets CB$(X)$ and providing new tools for multivalued mappings.
Abstract
In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new structural properties and fixed-point results for the multivalued counterparts are explored.