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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHEB_2020_21_2_a21,
     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/}
}
TY  - JOUR
AU  - V. V. Obukhovskii
AU  - S. V. Kornev
AU  - E. N. Getmanova
TI  - On topological characteristics for some classes of multivalued mappings
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 301
EP  - 319
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a21/
LA  - ru
ID  - CHEB_2020_21_2_a21
ER  - 
%0 Journal Article
%A V. V. Obukhovskii
%A S. V. Kornev
%A E. N. Getmanova
%T On topological characteristics for some classes of multivalued mappings
%J Čebyševskij sbornik
%D 2020
%P 301-319
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a21/
%G ru
%F CHEB_2020_21_2_a21
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/

[1] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “Topological methods in the fixed-point theory of multi-valued maps”, Russian Math. Surveys, 35:1 (1980), 65–143 | DOI | MR | Zbl

[2] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “Multivalued mappings”, J. Soviet Math., 24:6 (1984), 719–791 | DOI | MR | Zbl

[3] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, Introduction to the theory of multivalued mappings and differential inclusions, LIBROKOM, M., 2011 | MR

[4] K. Borsuk, Theory of retracts, PWN, Warsaw, 1967 | MR | Zbl

[5] S. V. Kornev, V. V. Obukhovskii, “On some versions of the topological degree theory for nonconvex-valued multimaps”, Trudy Mat. Fac. Voronezh Univ. (N.S.), 8, VGU, Voronezh, 2004, 56–74

[6] A. D. Myshkis, “Generalizations of the theorem on a fixed point of a dynamical system inside of a closed trajectory”, Mat. Sb. (N.S.), 34(76) (1954), 525–540 | Zbl

[7] J. Andres, L. Górniewicz, “Random topological degree and random differential inclusions”, Topol. Methods Nonlin. Anal., 40 (2012), 337–358 | MR | Zbl

[8] R. Bader, W. Kryszewski, “Fixed-point index for compositions of set-valued maps with proximally $\infty$-connected values on arbitrary ANR's”, Set-Valued Anal., 2 (1994), 459–480 | DOI | MR | Zbl

[9] R. E. Gaines, J. L. Mawhin, Coincidence degree and and nonlinear differential equations, Lect. Notes Math., 568, Springer, Berlin, 1977 | DOI | MR | Zbl

[10] L. Górniewicz, Topological fixed point theory of multivalued mappings, 2nd ed., Springer, Dordrecht, 2006 | MR | Zbl

[11] S. Hu, N. Papageorgiou, Handbook of multivalued analysis, v. I, Theory, Kluwer, Dordrecht, 1997 | MR | Zbl

[12] D. M. Hyman, “On decreasing sequences of compact absolute retracts”, Fund Math., 64 (1969), 91–97 | DOI | MR | Zbl

[13] M. Kamenskii, V. Obukhovskii, P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, Walter de Gruyter, Berlin — New York, 2001 | MR

[14] V. Obukhovskii, P. Zecca, N. V. Loi, S. Kornev, Method of guiding functions in problems of nonlinear analysis, Lect. Notes Math., 2076, Springer, Berlin–Heidelberg, 2013 | DOI | MR | Zbl

[15] E. Tarafdar, S. K. Teo, “On the existence of solutions of the equation $Lx \in Nx$ and a coincidence degree theory”, J. Austral. Math. Soc. (Ser. A), 28 (1979), 139–173 | DOI | MR | Zbl

[16] E. Tarafdar, P. Watson, X.-Z. Yuan, “Random coincidence degree theory with applications to random differential inclusions”, Comment. Math. Univ. Carolinae, 37 (1996), 725–748 | MR | Zbl