N*-Iteration Approach for Approximation of Fixed Points in Uniformly Convex Banach Space

Raghad I.  Sabri

doi:10.6180/jase.202508_28(8).0005

N*-Iteration Approach for Approximation of Fixed Points in Uniformly Convex Banach Space

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Raghad I. SabriThis email address is being protected from spambots. You need JavaScript enabled to view it.

Department of Applied Sciences, University of Technology-Iraq

Received: February 5, 2024
Accepted: September 17, 2024
Publication Date: October 26, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202508_28(8).0005

In this paper, a new iterative approach for approximating the fixed points (FPs) of Suzuki generalized nonexpansive (SGN) mapping as well as weak contractions, called the N* iteration approach, is presented. Furthermore, it is demonstrated analytically and numerically that the proposed approach converges to an FP for contraction map faster than some well-known and leading approaches. To support the main results, several non-trivial numerical examples are presented. Finally, the stability of the new iterative approach is confirmed. The results of this work improve and extend the corresponding results in the literature.

Keywords: Converge sequence, Fixed point, Iteration process, Suzuki’s generalized non-expansive mapping, Uniformly convex Banach space.

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