Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process

Year 2022, Volume: 5 Issue: 1, 35 - 39, 30.04.2022

Seyit Temir Öznur Korkut

https://doi.org/10.33187/jmsm.993823

Abstract

In this paper we introduce a new iteration process for approximation of fixed points. We numerically compare convergence behavior of our iteration process with other iteration process like M-iteration process. We also prove weak and strong convergence theorems for generalized $\alpha-$nonexpansive mappings by using new iteration process. Furthermore we give an example for generalized $\alpha-$nonexpansive mapping but does not satisfy $(C)$ condition.

Keywords

Uniformly convex Banach spaces, iteration processes, generalized $\alpha-$nonexpansive mappings, fixed point, convergence

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