Approximating common fixed points of countable families of strongly nonexpansive mappings

Abstract

We study the problem of approximating common fixed points of a countable infinite family of strongly nonexpansive mappings in Banach spaces. Using the obtained result, we deduce a strong convergence theorem for a countable infinite family of relatively nonexpansvie mappings. Applications to the convex feasibility problem and a proximal-type algorithm are also included.