Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals

Abstract: In this paper, we prove Krasnoselskii and Mann''s type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let be a sequence in [) satisfying Let . Define a sequence in C by and for . Then converges strongly to a common fixed point of . [Copyright &y& Elsevier]