Fixed points and common fixed points for orbit-nonexpansive mappings in metric spaces

TL;DR

This paper introduces an interlacing condition for families of operators in metric spaces, enabling new fixed point and common fixed point results based on orbit nonexpansivity and properties of closed balls.

Contribution

It presents a novel interlacing condition for operator families that generalizes fixed point results using orbit nonexpansivity in metric spaces.

Findings

Established fixed point theorems under the new interlacing condition

Derived common fixed point results for families of mappings

Extended fixed point theory using properties of closed balls in metric spaces

Abstract

In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric spaces. The innovative concept studied here deals with nonexpansivity conditions with respect to orbits and under assumptions that only depend on the features of the closed balls of the metric space.