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Matematicheskie Zametki, 2022, Volume 111, Issue 3, Pages 451–458
DOI: https://doi.org/10.4213/mzm13279 (Mi mzm13279) 		 
On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets

G. Z. Chelidzeab, A. N. Daneliac, M. Z. Suladzec

a Kutaisi International University
b Muskhelishvili Institute of Computational Mathematics
c Tbilisi Ivane Javakhishvili State University
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DOI: https://doi.org/10.4213/mzm13279
Abstract: We show that if every bounded set in a Banach space has a Chebyshev center, then the intersection of nested closed bounded sets in this space is nonempty in the case of a critical parameter value. This result generalizes previously obtained sufficient conditions for the nonemptiness of the intersection in the critical case. We also answer a question posed by G. Z. Chelidze and P. L. Papini for Banach spaces satisfying the Opial condition for the weak-$*$ topology.
Keywords: numerical parameter of a set in a normed space, nonemptiness of the intersection of nested sets, Chebyshev center, Opial weak-$*$ property.
Funding agency Grant number
Shota Rustaveli National Science Foundation FR-18-1599
The second author was supported by the Shota Rustaveli National Science Foundation of Georgia (SRNSFG) under grant no. FR-18-1599.
Received: 02.09.2021
Revised: 11.10.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 3, Pages 478–483
DOI: https://doi.org/10.1134/S0001434622030154
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: G. Z. Chelidze, A. N. Danelia, M. Z. Suladze, “On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets”, Mat. Zametki, 111:3 (2022), 451–458; Math. Notes, 111:3 (2022), 478–483
Citation in format AMSBIB
\Bibitem{CheDanSul22}
\by G.~Z.~Chelidze, A.~N.~Danelia, M.~Z.~Suladze
\paper On the Chebyshev Center and the Nonemptiness of the Intersection of Nested Sets
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 3
\pages 451--458
\mathnet{http://mi.mathnet.ru/mzm13279}
\crossref{https://doi.org/10.4213/mzm13279}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461275}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 3
\pages 478--483
\crossref{https://doi.org/10.1134/S0001434622030154}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128923278}
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