Ishikawa Iterative Process for a Pair of Single-valued and Multivalued Nonexpansive Mappings in Banach Spaces
Kritsana Sokhuma, Annop Kaewkhao · Fixed Point Theory and Applications · 2010
Abstract Let "Equation missing" be a nonempty compact convex subset of a uniformly convex Banach space "Equation missing", and let "Equation missing" and "Equation missing" be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that "Equation missing" and "Equation missing" for all "Equation missing". We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary "Equation missing" by "Equation missing", "Equation missing", where "Equation missing" and "Equation missing", "Equation missing" are sequences of positive numbers satisfying "Equation missing", "Equation missing", converges strongly to a common fixed point of "Equation missing" and "Equation missing"; that is, there exists "Equation missing" such that "Equation missing".