Vol. 22(2021) No. 2



  Existence of group nonexpansive retractions and ergodic theorems in topological groups
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Fixed Point Theory, Volume 22, No. 2, 2021, 455-464, July 1st, 2021

DOI: 10.24193/fpt-ro.2021.2.30

Authors: Ravi Agarwal, Donal O'Regan and Ebrahim Soori

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 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.

Key Words and Phrases: Fixed point, group nonexpansive mapping, topological group, retraction.

2010 Mathematics Subject Classification: 47H09, 47H10.

Published on-line: July 1st, 2021.

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