Convergence of AA-Iterative Algorithm for Generalized <i>α</i>-Nonexpansive Mappings with an Application

Abstract

The aim of this paper is to approximate the fixed points of generalized α-nonexpansive mappings using AA-iterative algorithm. We establish some weak and strong convergence results for generalized α-nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the AA-iterative algorithm converges faster than some others algorithms for generalized α-nonexpansive mappings. Lastly, using the AA-iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

Keywords

• <i>AA</i>-iteration
• generalized α-nonexpansive mapping
• fixed point
• Banach space