On some generalizations of the Mönch, Sadovskiĭ and Darbo fixed point theorems

Abstract

The Monch fixed point theorem and the corresponding continuation theorem of Leray–Schauder type for admissible set-valued maps defined on Frechet spaces is proved. The most conceivably simplistic definition of condensing set-valued maps in terms of functional relation, which binds an MNC of the image of a subset under the operator with the measure of that set, is given. This approach generalizes in particular the Sadovskiĭ and Darbo theorems beyond many other results contained in the literature of the subject.