Fixed point for a generalized Lipschitzian semigroup and demiclosed criteria (Q1125484)

The main result of the paper is a fixed point theorem (Theorem 3.1) for a semigroup of generalized contractions (called ``Lipschitzian'' by the authors) on a Banach space, whose uniformity of normal structure satisfies a certain inequality with respect to the coefficients involved in the generalized contraction condition. The demiclosedness property for this class of mappings in a uniformly convex Banach space is also studied.