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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 7, Pages 1167–1174 (Mi zvmmf4715)  

This article is cited in 3 scientific papers (total in 3 papers)

Minimum of a functional in a metric space and fixed points

A. V. Arutyunova, B. D. Gel'manb

a Peoples Friendship University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia
b Voronezh State University, Universitetskaya pl. 1, Voronezh, 394693, Russia

Abstract: The existence of minimizers is examined for a function defined on a metric space. Theorems are proved that assert the existence of minimizers, and examples of the functions for which these theorems are valid are given. Then, these theorems are applied to proving theorems on fixed points of univalent and multivalued mappings of metric spaces. Finally, coincident points of two mappings are examined.

Key words: minimum of function, contraction mapping, fixed point, solution to equation.

Full text: PDF file (1051 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:7, 1111–1118

Bibliographic databases:

UDC: 519.626
Received: 06.11.2008

Citation: A. V. Arutyunov, B. D. Gel'man, “Minimum of a functional in a metric space and fixed points”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1167–1174; Comput. Math. Math. Phys., 49:7 (2009), 1111–1118

Citation in format AMSBIB
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\by A.~V.~Arutyunov, B.~D.~Gel'man
\paper Minimum of a~functional in a~metric space and fixed points
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 7
\pages 1167--1174
\mathnet{http://mi.mathnet.ru/zvmmf4715}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 7
\pages 1111--1118
\crossref{https://doi.org/10.1134/S0965542509070045}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70349957957}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Arutyunov, “Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points”, Proc. Steklov Inst. Math., 291 (2015), 24–37  mathnet  crossref  crossref  isi  elib
    2. Zhukovskiy S.E., “Comparison of Some Types of Locally Covering Mappings”, Fixed Point Theory, 17:1 (2016), 215–222  mathscinet  zmath  isi
    3. Arutyunov A.V., Gel'man B.D., Zhukovskiy E.S., Zhukovskiy S.E., “Caristi-Like Condition. Existence of Solutions to Equations and Minima of Functions in Metric Spaces”, Fixed Point Theory, 20:1 (2019), 31–57  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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