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Sbornik: Mathematics, 2019, Volume 210, Issue 6, Pages 836–861
DOI: https://doi.org/10.1070/SM8997 (Mi sm8997) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Connectedness of the solution sets of inclusions

E. S. Zhukovskiy

Derzhavin Tambov State University, Tambov, Russia
English version PDF (625 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM8997
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).
Received: 22.07.2017 and 09.12.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 6, Pages 82–110
DOI: https://doi.org/10.4213/sm8997
Bibliographic databases:
Document Type: Article
UDC: 517.988.6
MSC: 39B70, 45D05
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 2 articles:
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    References:62
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