Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces

Abstract

We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.