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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 493, Pages 13–17
DOI: https://doi.org/10.31857/S2686954320040220 (Mi danma87) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences

Yu. N. Zakharyan, T. N. Fomenko

Lomonosov Moscow State University, Moscow, Russian Federation
Full-text PDF (136 kB) Citations (5)
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DOI: https://doi.org/10.31857/S2686954320040220
Abstract: A theorem on the zero existence preservation for a parametric family of multivalued $(\alpha,\beta)$-search functionals on an open subset of a metric space is proved. Several corollaries on the existence preservation for preimages of a closed subspace, for coincidence points, and for common fixed points under the action of a parametric family (a number of families) of mappings are obtained. The notion of a Zamfirescu-type pair of mappings is introduced, and a coincidence theorem for such pairs of mappings is obtained. In addition, a theorem on the coincidence existence preservation for a parametric family of such pairs of mappings is obtained. The obtained results imply several well-known theorems.
Keywords: parametric family of functionals, multivalued mapping, fixed point, coincidence point, Zamfirescu mapping, Zamfirescu-type pair of mappings preservation of coincidence existence, parametric family of mappings.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics
This work was performed within the research directions of the Moscow Center of Fundamental and Applied Mathematics.
Presented: S. V. Matveev
Received: 23.05.2020
Revised: 23.05.2020
Accepted: 02.06.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 1, Pages 272–275
DOI: https://doi.org/10.1134/S1064562420040225
Bibliographic databases:
Document Type: Article
UDC: 515.124, 515.126.4, 515.126.83
Language: Russian
Citation: Yu. N. Zakharyan, T. N. Fomenko, “Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences”, Dokl. RAN. Math. Inf. Proc. Upr., 493 (2020), 13–17; Dokl. Math., 102:1 (2020), 272–275
Citation in format AMSBIB
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\transl
\jour Dokl. Math.
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