Convergence of implicit iterative process with errors for a finite family of asymptotically nonexpansive mappings.(English)Zbl 1136.47043

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results by H. H. Bauschke, S. Reich, Z.-H. Sun, R. Wittmann, and others.

MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H05 Monotone operators and generalizations 49M05 Numerical methods based on necessary conditions