# Fixed Point of A New Type Nonself Total Asymptotically Nonexpansive Mappings in Banach Spaces

## TL;DR

This paper introduces a new class of nonself total asymptotically nonexpansive mappings in Banach spaces and establishes convergence theorems for finding their common fixed points using an iterative process.

## Contribution

It proposes a novel concept of nonself total asymptotically nonexpansive mappings and proves convergence theorems for their fixed points in Banach spaces.

## Key findings

- Established weak and strong convergence theorems.
- Provided an example demonstrating applicability.
- Extended fixed point theory for new mapping classes.

## Abstract

In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for computing common fixed points of two nonself total asymptotically nonexpansive mappings are established in the framework of Banach spaces. Finally, we give an example which show that our theorems are applicable.