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On New Iterative Algorithm for Numerical Reckoning Fixed Points of Weak Contraction Mapping in Bananch Spaces and Its Rate of Convergence

Year: 2024

Type: article

Abstract: This paper introduces a novel three-step iterative algorithm designed to approximate fixed points of nonlinear self-mappings within a specific class of weak contractions in Banach spaces. Additionally, we explore and compare the convergence rates of the Mann, Ishikawa, and Noor iterative algorithms with the newly proposed one. The results indicate that the proposed algorithm achieves faster convergence compared to the aforementioned iterative methods. Furthermore, we present two numerical examples computed using MATLAB to illustrate our findings, demonstrating the approximated fixed points. MSC [2010]: 47J25; 47N20; 65J15.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.13969433

Authors: SHRIJANA DHAKAL, SANTOSH GHIMIRE, MADHAV PRASAD POUDEL

Institutions: Tribhuvan University, Institute of Engineering, Pulchowk Campus, Pokhara University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6968083573

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