Semi-asymptotic non-expansive actions of semi-topological semigroups (Q2787643)

The paper contains an extension of Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. The concept of the semi-asymptotic non-expansive action of semi-topological semigroups is defined. One of the main results is the following Corollary. Let \(K\) be a non-empty, compact convex subset of a Banach space \(E\) and \(S\) be an amenable discrete semigroup which acts on \(K\) separately continuous and left semi-asymptotic non-expensive. Then \(S\) has a common fixed point in \(K\).