Abstract
We establish generalized fixed point theorems of Leray-Schauder type for compact or condensing multifunctions 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 Gorniewicz 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
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