Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators

Abstract

In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (\(\overline{C}\)) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.

Keywords

• asymptotically quasi-nonexpansive in the intermediate sense random operator
• implicit random iteration process with errors
• common random fixed point
• strong convergence
• separable uniformly convex Banach space