Weak and strong convergence theorems for a finite family of non-lipschitzian mappings in Banach spaces

Abstract

The purpose of this paper is to study a new iterative scheme for a finite family of asymptotically nonexpansive mappings in the intermediate sense. Weak and strong convergence theorems for the iterative scheme in a uniformly convex Banach space are established under some conditions which are weaker than demicompactness or completely continuous. Our results improve and generalize the recent known results in the literature. © 2010 Pleiades Publishing, Ltd.