Existence and Structure of the Common Fixed Points Based on TVS

Abstract

In this paper, we investigate the common fixed point property for commutative nonexpansive mappings on  $\tau$-compact convex sets in normed and Banach spaces, where $\tau$ is a Hausdorff topological vector space topology
that is weaker than the norm topology.
As a consequence of our main results, we obtain that the set of common fixed points of any commutative family
 of nonexpansive self-mappings of a nonempty $clm$-compact (resp. weak* compact) convex subset $C$ of $L_1(\mu)$ with a $\sigma$-finite $\mu$ (resp. the James space $J_0$) is a nonempty nonexpansive retract of $C$.