Convergence Theorems of Nonself Nearly Asymptotically Nonexpansive Mappings for Common Fixed Points in Banach Spaces

Abstract

Solving problems through fixed point is a powerful tool in mathematics. In this paper we study convergence theorems for two nonself nearly asymptotically nonexpansive mappings. Specifically, we take uniformly convex Banach space for two nonself mappings and an iteration process to find convergence of common fixed point. In this process we prove approximate fixed point results. We also prove strongly convergence theorems for common fixed point and weakly convergence theorem for common fixed point. The research probably involves designing specific iterative schemes that generates sequences that converges to the common fixed point. Analysing the convergence of these schemes is a crucial part of the work. This study contributes to the broader field of fixed point theory by extending existing results to a more general class of mappings, offering insights into the behaviour of nearly asymptotically nonexpansive mappings in the context of common fixed point problems.