Existence of group nonexpansive retractions and ergodic theorems in topological groups

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

Existence of group nonexpansive retractions and ergodic theorems in topological groups

Functional Analysis 2021-04-27 v6

Authors: Ebrahim Soori , Ravi P. Agarwal , Donal O'Regan

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 $P_{i}T_{i} = T_{i}P_{i} = P_{i}$ .

Keywords

topological groups group nonexpansive mappings group nonexpansive retractions compact subsets fixed points

Cite

@article{arxiv.1801.05322,
  title  = {Existence of group nonexpansive retractions and ergodic theorems in topological groups},
  author = {Ebrahim Soori and Ravi P. Agarwal and Donal O'Regan},
  journal= {arXiv preprint arXiv:1801.05322},
  year   = {2021}
}

Comments

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

Existence of group nonexpansive retractions and ergodic theorems in topological groups

Abstract

Keywords

Cite

Comments

Related papers