Convergence on Kirk Iteration of Cesàro Means for Asymptotically Nonexpansive Mappings

This article addresses the convergence of iteration sequences in Cesàro means for asymptotically nonexpansive mappings. Specifically, this study explores the behavior of Kirk iteration in the Cesàro means in the context of uniformly convex and reflexive Banach spaces equipped with uniformly Gâteaux differentiable norms. The focus is to determine the conditions under which the Kirk iteration sequence converges strongly or weakly to a fixed point. Finally, some examples are given in this article to demonstrate the advantages of the preferred iteration method and to verify the results obtained.