Abstract
Let E be a real reflexive Banach space which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed convex and bounded subset of E has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a common zero of a countably infinite family of alpha-inverse strongly accretive mappings are proved. Related results deal with strong convergence of theorems to a common fixed point of a countably infinite family of strictly pseudocontractive mappings. (C) 2008 Elsevier Ltd. All rights reserved.