Generalized Leray-Schauder principles for condensing admissible multifunctions

Abstract

We establish generalized fixed point theorems of Leray-Schauder type for compact or condensing multifunction in very general classes. Those classes contain composites of Kakutani maps, acyclic maps, approachable maps, u.s.c. maps with Rδ-values, the O'Neill maps, the Górniewicz type maps, the Dzedzej type maps, and many others. Our arguments are elementary in the sense that without any recourse to degree theory or theory of homotopy-extensions.