Locating Common Fixed Points of Nonlinear Representations of Semigroups

Abstract

This paper is concerned with the problem of nding common xed points for a
family of Bregman relatively weak nonexpansive mappings. The motivation is due to our nding
of some gaps in a paper of K. S. Kim (Nonlinear Analysis, 73 (2010), 3413-3419), where the
author was developing a hybrid iterative scheme for locating common xed points of a nonlinear
representation of a left reversible semigroup. After a brief discussion about the gaps and why
they are fatal, we present a new approach by using Bergman type nonexpansive mappings. A
correct version of Kim's convergence theorem is given as a consequence of our new results, which
also improve and extend some recent results in the literature.