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Mat. Sb., 2019, Volume 210, Number 6, Pages 82–110 (Mi msb8997)  

Connectedness of the solution sets of inclusions

E. S. Zhukovskiy

Derzhavin Tambov State University, Tambov, Russia

Abstract: A research scheme for investigating the connectedness of the set of solutions of an inclusion in a topological space is proposed. It is applied to analyze the fixed-point set of a Volterra set-valued map in the space of continuous functions $C$; conditions for it to be connected in the norm and weak topology of $C$ are obtained. On this basis conditions are found which ensure that the solution set of Hammerstein's delay integral inclusion is connected.
Bibliography: 14 titles.

Keywords: connectedness, topological space, Volterra set-valued map, fixed point.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00553-а
17-41-680975-р_а
17-51-12064-ННИО_а
Ministry of Education and Science of the Russian Federation 3.8515.2017/БЧ
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 17-01-00553-a, 17-41-680975-p_a and 17-51-12064-ННИО_а); the research in § 3.5 was supported by the Ministry of Education and Science of the Russian Federation (assignment no. 3.8515.2017/БЧ).


DOI: https://doi.org/10.4213/sm8997

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English version:
Sbornik: Mathematics, 2019, 210:6, 836–861

Bibliographic databases:

UDC: 517.988.6
MSC: 39B70, 45D05
Received: 22.07.2017 and 09.12.2018

Citation: E. S. Zhukovskiy, “Connectedness of the solution sets of inclusions”, Mat. Sb., 210:6 (2019), 82–110; Sb. Math., 210:6 (2019), 836–861

Citation in format AMSBIB
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