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Some convergence results using a new iteration process for generalized nonexpansive mappings in Banach spaces

Seyit Temir

Department of Mathematics, Art and Science Faculty, Adıyaman University, 02040 Adıyaman, Turkey

E-mail Address: seyittemir@adiyaman.edu.tr

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and

Öznur Korkut

Department of Mathematics Graduate Education Institute, Adıyaman University, 02040 Adıyaman, Turkey

E-mail Address: oevrenxxx79@hotmail.com

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https://doi.org/10.1142/S1793557123500778Cited by:2 (Source: Crossref)

Abstract

In this paper, we introduce a new iterative process for approximation fixed points. We show the stability of our proposed iteration process. We prove some weak and strong convergence theorems for generalized $α$ -nonexpansive mappings in the framework of uniformly convex Banach spaces. We also provide an example of a generalized $α$ -nonexpansive mapping to show numerically that our iteration is faster than various prominent iteration processes.

Communicated by N. C. Wong

Keywords:

AMSC: 47H09, 47H10

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