Weak and strong convergence theorems for a finite family of generalized asymptotically quasi-nonexpansive mappings

Abstract

In this paper, we introduce a new iterative scheme for finding a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive mappings in a uniformly convex Banach space. We establish weak and strong convergence theorems. Our main results improve and extend the corresponding ones obtained in Schu (1991) [J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mapping, J. Math. Anal. Appl. 159 (1991) 407413] and many others. © 2010 Elsevier Ltd. All rights reserved.