Mixed Non-Expansive and Potentially Expansive Properties of a Class of Self-Maps in Metric Spaces

TL;DR

This paper explores a class of self-maps in metric spaces that exhibit mixed non-expansive, contractive, and potentially expansive properties, relevant to real-world problems involving distance constraints.

Contribution

It introduces a novel analysis of self-maps with mixed properties in metric spaces, expanding understanding of their behavior under various distance conditions.

Findings

Characterization of self-maps with mixed properties

Conditions under which these maps are contractive or expansive

Potential applications in real-world problems involving distance constraints

Abstract

This paper investigates self-maps T from X to X which satisfy a distance constraint in a metric space which mixed point-dependent non-expansive properties, or in particular contractive ones, and potentially expansive properties related to some distance threshold. The above mentioned constraint is feasible in certain real -world problems.