Some remarks on the set of common fixed points of one-parameter semigroups of nonexpansive mappings in Banach spaces with the Opial property

Abstract

In this paper, we discuss the necessary and sufficient condition for common fixed points of one-parameter nonexpansive semigroups in Banach spaces with the Opial property. We next prove the convergence theorem to a common fixed point. Finally, we discuss the existence of nonexpansive retraction onto the set of common fixed points. In these theorems, we may not assume that the strict (uniform) convexity of a Banach space.