Strong convergence of Browder’s type iterations for left amenable semigroups of Lipschitzian mappings in Banach spaces

Abstract.

We study an iterative scheme of Browder’s type for a semigroup of Lipschitzian mappings satisfying some uniform Lipschitzian condition, from a compact convex subset C of a smooth Banach space into C, with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup. The results presented in this paper generalize the corresponding results of Lau, Miyake and Takahashi [Nonlinear Anal. 67 (2007), 1211–1225].