ON THE CONVERGENCE OF MODIFIED EXPLICIT ITERATIONS WITH ERRORS FOR FINITE FAMILIES OF NON-SELF MAPPINGS IN BANACH SPACES

R. A. Rashwan (Egypt) and A. A. Abdel Hakim (Egypt)

Received July 28, 2007

Abstract

In this paper, we introduce two explicit one-step iterative procedures and use them to obtain weak and strong convergence theorems to a common fixed point of a finite family of non-self asymptotically quasi-nonexpansive mappings in real uniformly convex Banach spaces. Also, we establish weak and strong convergence theorems to a common fixed point of a finite family of non-self asymptotically nonexpansive  mappings with respect to a sunny nonexpansive retraction P in real smooth uniformly convex Banach spaces. Our results extend and improve some known results.

Keywords and phrases: non-self asymptotically nonexpansive mappings, non-self asymptotically quasi-nonexpansive mappings, non-self uniformly L-Lipschitzian mappings, common fixed points, explicit iterative process, uniformly convex Banach spaces.