Existence of sunny nonexpansive retractions and approximation of fixed points of a representation of nonexpansive mappings

This paper presents an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth uniformly convex Banach space with respect to a left-regular sequence of means defined on a subset of ι^∞(S). The main results are to establish an existence theorem of a sunny nonexpansive retraction and to create an algorithm for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces.