Halpern iteration for a finite family of quasinonexpansive mappings on a complete geodesic space with curvature bounded above by one

TL;DR

This paper establishes a strong convergence theorem for the Halpern iteration scheme applied to a finite family of quasinonexpansive mappings in a complete geodesic space with curvature bounded above by one, advancing fixed point theory in curved spaces.

Contribution

It introduces a new convergence result for Halpern iteration in curved spaces, extending fixed point theory to non-linear geometric contexts.

Findings

Proves strong convergence of Halpern iteration in curved spaces.

Extends fixed point results to quasinonexpansive mappings.

Applicable to spaces with curvature bounded above by one.

Abstract

In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by one.