ON NEW ITERATIVE ALGORITHM FOR NUMERICAL RECKONING FIXED POINTS OF WEAK CONTRACTION MAPPING IN BANANCH SPACES AND ITS RATE OF CONVERGENCE

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.