An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces
Shenghua Wang, Lanxiang Yu, Baohua Guo · Fixed Point Theory and Applications · 2008
Abstract Let "Equation missing" be a nonempty closed convex subset of a reflexive Banach space "Equation missing" with a weakly continuous dual mapping, and let "Equation missing" be an infinite countable family of asymptotically nonexpansive mappings with the sequence "Equation missing" satisfying "Equation missing" for each "Equation missing", "Equation missing", and "Equation missing" for each "Equation missing". In this paper, we introduce a new implicit iterative scheme generated by "Equation missing" and prove that the scheme converges strongly to a common fixed point of "Equation missing", which solves some certain variational inequality.