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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2018, Volume 24, Number 1, Pages 93–105
DOI: https://doi.org/10.21538/0134-4889-2018-24-1-93-105
(Mi timm1499)
 

This article is cited in 11 scientific papers (total in 11 papers)

On fixed points of multivalued mappings in spaces with a vector-valued metric

E. S. Zhukovskiyab, E. A. Panasenkoa

a Tambov State University named after G.R. Derzhavin
b Peoples Friendship University of Russia
References:
Abstract: Nadler's theorem on a fixed point of a multivalued mapping is extended to spaces with a vector-valued metric. A vector-valued metric is understood as a mapping with the properties of a usual metric and values in a linear normed ordered space. We prove an analog of Nadler's theorem and apply it to a system of integral inclusions in a space of summable functions. Then we study a boundary value problem with multivalued conditions for systems of functional differential equations by means of reduction to a system of integral inclusions. Conditions for the existence of solutions are obtained and estimates of the solutions are given. The existence conditions do not contain the convexity requirement for the values of the multivalued function generating a Nemytskii operator.
Keywords: space with a vector-valued metric, contracting multivalued mapping, fixed point, integral inclusion.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 3.8515.2017/БЧ
Russian Foundation for Basic Research 17-01-00553
16-01-00386
Russian Science Foundation 17-11-01168
Received: 09.10.2017
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, Volume 305, Issue 1, Pages S191–S203
DOI: https://doi.org/10.1134/S0081543819040199
Bibliographic databases:
Document Type: Article
UDC: 515.124+517.988.6+517.911.5
MSC: 54E35, 54H25, 34K09
Language: Russian
Citation: E. S. Zhukovskiy, E. A. Panasenko, “On fixed points of multivalued mappings in spaces with a vector-valued metric”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 1, 2018, 93–105; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S191–S203
Citation in format AMSBIB
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\by E.~S.~Zhukovskiy, E.~A.~Panasenko
\paper On fixed points of multivalued mappings in spaces with a vector-valued metric
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 93--105
\mathnet{http://mi.mathnet.ru/timm1499}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-1-93-105}
\elib{https://elibrary.ru/item.asp?id=32604047}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 305
\issue , suppl. 1
\pages S191--S203
\crossref{https://doi.org/10.1134/S0081543819040199}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073510882}
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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