Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

TL;DR

This paper establishes fixed point theorems and iterative methods for a broad class of nonlinear mappings in uniformly convex hyperbolic spaces, extending existing results and providing convergence guarantees.

Contribution

It introduces a new fixed point theorem and iterative scheme for total asymptotically nonexpansive mappings in hyperbolic spaces, generalizing prior work.

Findings

Established strong and del-convergence results.

Extended fixed point theory to hyperbolic spaces.

Generalized multi-step iteration methods.

Abstract

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu [4] in such setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and del-convergence results which extend and generalize various corresponding results announced in the current literature.