Existence of group nonexpansive retractions and ergodic theorems in topological groups

Ebrahim Soori; Ravi P. Agarwal; Donal O'Regan

paper

Existence of group nonexpansive retractions and ergodic theorems in topological groups

arXiv:1801.05322

Abstract

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 $\sc = \{T_{i} : i \in I \}$ as a family of the group nonexpansive mappings on $C$ . Also we study the existence of group nonexpansive retractions $P_{i}$ from $C$ onto $\text{Fix}(\sc)$ such that $P_{i} T_{i} = T_{i} P_{i} = P_{i}$ .

13 pages. arXiv admin note: text overlap with arXiv:1708.08883. Accepted in the journal "Fixed point theory"