Abstract
We define a topological characteristic, the fixed point index with respect to a convex closed subset of a Banach space for a class of completely fundamentally restrictible multivalued maps which can be represented as a composition of maps with aspheric values. This class includes, in particular, maps which are condensing with respect to a monotone nonsingular measure of noncompactness. Maps of this type naturally arise in the study of nonlinear systems with impulse effects. Applications of the index to some fixed point theorems are considered.
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Funding
The work of E.N. Getmanova and S.V. Kornev was financially supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of a state assignment in the field of science (project no. FZGF-2020-0009). The results in paragraph 4 were obtained by V.V. Obukhovsky with the support of the Russian Science Foundation (project no. 20-11-20131) at the Institute for Control Problems named after V.A. Trapeznikov of RAS.
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Dedicated to the 90th anniversary of the birth of Yuri Grigorievich Borisovich
Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 64–77.
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Obukhovskii, V.V., Kornev, S.V. & Getmanova, E.N. On the Relative Fixed Point Index for a Class of Noncompact Multivalued Maps. Russ Math. 65, 48–59 (2021). https://doi.org/10.3103/S1066369X2105008X
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DOI: https://doi.org/10.3103/S1066369X2105008X