On topological groups with an approximate fixed point property

Abstract

A topological group $G$ has the Approximate Fixed Point (AFP) property on a bounded convex subset $C$ of a locally convex space if every continuous affine action of $G$ on $C$ admits a net $\left(x_i\right)$, $x_i\in C$, such that $x_i-g{x}_i⟶0$ for all $g\in G$. In this work, we study the relationship between this property and amenability.

Key words
Amenable groups; approximate fixed point property; Følner property; Reiter property