Geodesic
On topological characteristics for some classes of multivalued mappings
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 301-319

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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. 
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     author = {V. V. Obukhovskii and S. V. Kornev and E. N. Getmanova},
     title = {On topological characteristics for some classes of multivalued mappings},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {301--319},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a21/}
}
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V. V. Obukhovskii; S. V. Kornev; E. N. Getmanova. On topological characteristics for some classes of multivalued mappings. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 301-319. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a21/