The fixed point property for a class of nonexpansive maps in L\sp\infty(Ω,Σ,μ)

Abstract

For a finite and positive measure space $(\Omega ,\Sigma ,\mu )$ and any weakly compact convex subset of $L\sp\infty(Ω,Σ,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained for the space $C(\Omega )$. An illustrative example is given.

4 pages