A Four-Step Iteration Scheme to Approximate Fixed Points of Generalized (α, β)-Nonexpansive Type 1 Mappings with Application

Abstract

In this paper, we introduce a four-step iteration scheme for approximating fixed points of generalized (α, β)-nonexpansive type 1 mapping. We prove the convergence and stability results for contractive-like mapping in uniformly convex Banach space. We also prove weak and strong convergence results for generalized (α, β)-nonexpansive type 1 mapping. We provide numerical examples to show that this scheme is faster than Agarwal, Abbas, Thakur, Ullah and S^(⋆⋆) -iteration scheme. We used this iteration method to find the solution of a nonlinear integral equation.