Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.
"Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces." Abstr. Appl. Anal. 2013 (SI60) 1 - 9, 2013. https://doi.org/10.1155/2013/264910