A New Fixed Point Iterative Method for Weak Contraction Mapping and Its Application to Integral Equations

Abstract

This study aims to develop a novel approximation algorithm for estimating fixed points of weak contraction mappings in Banach spaces. We propose an iterative method that demonstrates strong convergence and stability for weak contraction mappings in closed and convex subsets of Banach spaces. Theoretical analysis proves that the proposed algorithm achieves a faster convergence rate compared to existing iterative schemes, thereby improving upon previous results. Additionally, we apply our results to estimate solutions for integral equa tions as its practical utility. Finally, numerical simulations are provided to validate the theoretical findings and highlight the efficiency of the algorithm.