Fixed point approximation of nonexpansive mappings and its application to delay integral equation

In this paper, we introduce a modified AG iterative scheme for approximating the fixed point of nonexpansive mappings in a uniformly convex Banach space (UCBS). The convergence and stability are proved for the proposed iterative scheme for the class of Reich–Suzuki nonexpansive mappings. Our results generalize many comparable results in the literature. This work shows improved convergence rate, faster iteration, and enhanced convergence efficiency. Finally, we compare our scheme with the Picard, Mann, Noor, Picard–Mann, M, and Thakur iterative schemes with the help of numerical examples that demonstrate faster convergence.