Efficient fixed-point iteration for generalized nonexpansive mappings and its stability in Banach spaces-Reference-Cited by-同舟云学术

Efficient fixed-point iteration for generalized nonexpansive mappings and its stability in Banach spaces

Published:2022-12-31 Issue:1 Volume:20 Page:1753-1769
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Ali Danish¹,Hussain Aftab²,Karapinar Erdal³⁴⁵,Cholamjiak Prasit⁶

Affiliation:

1. Department of Mathematics , Facutly of Natural Science , Khawaja Fareed University of Engineering and Technology , 64100 Rahim Yar Khan , Pakistan

2. Department of Mathematics , King Abdulaziz University , P.O. Box 80203 , Jeddah 21589 , Saudi Arabia

3. Division of Applied Mathematics , Thu Dau Mot University , Binh Duong Province , Vietnam

4. Department of Medical Research , China Medical University Hospital , China Medical University , 40402, Taichung , Taiwan

5. Department of Mathematics , Çankaya University , 06790, Etimesgut , Ankara , Turkey

6. School of Science , University of Phayao , Phayao 56000 , Thailand

Abstract

Abstract The aim of this article is to design a new iteration process for solving certain fixed-point problems. In particular, we prove weak and strong convergence theorems for generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. In addition, we discuss the stability of the solution under mild conditions. Further, we provide some numerical examples to indicate that the proposed method works properly.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0461/pdf

Reference23 articles.

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4. K. Ullah and M. Arshad, New iteration process and numerical reckoning fixed points in Banach, U.P.B. Sci. Bull. Ser. A 79 (2017), 113–122.

5. K. Ullah and M. Arshad, New three-step iteration process and fixed point approximation in Banach spaces, J. Linear. Topol. Algebra 7 (2018), 87–100.

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