Continuous selections for multivalued mappings with closed convex images and applications
Some extensions of the Michael selection theorem are studied. Introducing notions of \(r\)-lower semicontinuity (for \(0<r<1)\) and partial lower semicontinuity (these concepts are too involved to be described here), the authors show that given a paracompact space \(X\), a Banach space \(Y\) if a set-valued \(F:X\to Y\) with closed convex values is \(r\)-lower semicontinuous (or partial lower semicontinuous), then it admits a continuous selection. Usual consequences concerning the existence of fixed points or solutions to differential inclusions involving maps of the above type follow.
scientific article; zbMATH DE number 1563468
scientific article