Fixed points of nonexpansive self-maps of a compact metric space (Q1822340)

\textit{T. Mitchell} [Kodai Math. Sem. Rep. 22, 322-323 (1970; Zbl 0224.47020)] proved that if X is a compact convex subset of a Banach space, and G is a left reversible semigroup of nonexpansive self-maps of X, then X contains a common fixed point of G. In this note it is shown that X can be taken as a compact metric space in which there exists for every pair x,y\(\in X\) a \(z\in X\) such that \(d(z,u)\leq (d(x,u)+d(y,u))\) for all \(u\in X\).