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.
Keywords:topological degree, multivalued mapping, random mapping, random fixed point, random coincidence point, random index of fixed points, degree of coincidence, measure of noncompactness, condensing operator.