Existence of group nonexpansive retractions and ergodic theorems in topological groups

摘要

Suppose that?G?is a topological group and?C?a compact subset of?G. In this paper we define group nonexpansive mappings and then we consider?S = {Ti?: i ∈ I}?as a family of the group nonexpansive mappings on?C. Also we study the existence of group nonexpansive retractions?Pi?from?C?onto Fix(S) such that?PiTi?= TiPi?= Pi.