On topological characteristics for some classes of multivalued mappings

Abstract

In the paper the topological characteristics of multivalued mappings that can be represented
as a finite composition of mappings with aspherical values are considered. For such random
mappings, condensing with respect to some abstract measure of noncompactness, a random
index of fixed points is introduced, its properties are described and applications to fixed-point
theorems are given. The topological coincidence degree is defined for a condensing pair consisting
of a linear Fredholm operator of zero index and a multivalued mapping of the above class. In
the last section possibilities of extending this theory to random condensing pairs are shown.