Strong Convergence Theorems for a Finite Family of Quasi-nonexpansive and Asymptotically Quasi-nonexpansive Mappings in Banach spaces

Abstract

In this paper, we give the sufficient condition for strong convergence of finite step iteration sequences with errors to a common fixed point for a pair of a finite family of quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in closed convex subset of a Banach spaces. The results presented in this paper generalize, improve unify the corresponding results in [1, 2, 4, 5, 9, 10]. Keywords: Quasi-nonexpansive mapping; asymptotically quasi nonexpansive map-ping; common fixed point; multi-step iteration scheme. 2010 Mathematics Subject Classification 47H09; 47H10.