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Matematicheskie Zametki, 2020, Volume 108, Issue 6, Pages 837–850
DOI: https://doi.org/10.4213/mzm12932
(Mi mzm12932)
 

This article is cited in 5 scientific papers (total in 5 papers)

Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences

Yu. N. Zakharyan, T. N. Fomenko

Lomonosov Moscow State University
Full-text PDF (513 kB) Citations (5)
References:
Abstract: A theorem on the preservation of the existence of zeros under the change of the parameter in a one-parameter family of $(\alpha,\beta)$-search functionals on an open subset of a metric space is proved. The following corollaries of this theorem are presented: on the preservation of the existence of preimages of a given closed subspace in a parametric family of multivalued mappings of metric spaces; on the preservation of the existence of coincidence points in a finite collection of two or more families of multivalued mappings of metric spaces; on the preservation of the existence of common fixed points in a collection of families of multivalued mappings to itself of a metric space. As a simple particular case, the Frigon–Granas theorem (1994) on fixed points of a contraction family of multivalued mappings is obtained.
Keywords: search functional, family of set-valued functionals, fixed point, coincidence point, contraction family of mappings.
Received: 07.05.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 6, Pages 802–813
DOI: https://doi.org/10.1134/S0001434620110231
Bibliographic databases:
Document Type: Article
UDC: 515.124+515.126.4+515.126.83
Language: Russian
Citation: Yu. N. Zakharyan, T. N. Fomenko, “Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences”, Mat. Zametki, 108:6 (2020), 837–850; Math. Notes, 108:6 (2020), 802–813
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm12932
  • https://doi.org/10.4213/mzm12932
  • https://www.mathnet.ru/eng/mzm/v108/i6/p837
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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