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Fixed Point Theorems for Lipspchitzian Semigroups

Abstract Let U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sup s has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sup s