Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps

摘要

The aim of this paper is to prove strong convergence of a modified implicit iteration process to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings. An immediate corollary of our theorems provides an affirmative response to a question raised by Xu and Ori [H.K. Xu, R. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].