Fixed points of asymptotically regular semigroups in Banach spaces

Abstract

In this paper we study in Banach spaces the existence of fixed points of (nonlinear) asymptotically regular semigroups. We establish for these semigroups some fixed point theorems in spaces with weak uniform normal structure, in a Hilbert space, inLp spaces, in Hardy spacesHp and in Sobolev spacesWr.p for 1<p<∞ andr≥0, in spaces with Lifshitz’s constant greater than one. These results are the generalizations of [8, 10, 16].