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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 4(190), Pages 169–198 (Mi umn3797)  

This article is cited in 6 scientific papers (total in 6 papers)

A converse to the principle of contracting maps

V. I. Opoitsev


Abstract: In the paper we give an account of several versions of a converse to the principle of contracting maps. More exactly, we answer the question: under what conditions on an operator mapping a complete metric space into itself is there an equivalent metric in which the operator is contracting? We also consider the more general problem about the existence of an equivalent metric in which families and semigroups of operators are contracting, and we indicate connections of this problem with the theory of the stability of motion. A similar problem (about the existence of an equivalent norm) can be raised in the case of a Banach space.

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English version:
Russian Mathematical Surveys, 1976, 31:4, 175–204

Bibliographic databases:

UDC: 517.4
MSC: 47D03, 46Bxx, 14Dxx
Received: 18.10.1974

Citation: V. I. Opoitsev, “A converse to the principle of contracting maps”, Uspekhi Mat. Nauk, 31:4(190) (1976), 169–198; Russian Math. Surveys, 31:4 (1976), 175–204

Citation in format AMSBIB
\Bibitem{Opo76}
\by V.~I.~Opoitsev
\paper A~converse to~the~principle of~contracting maps
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 4(190)
\pages 169--198
\mathnet{http://mi.mathnet.ru/umn3797}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=420591}
\zmath{https://zbmath.org/?q=an:0335.54025|0351.54025}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 4
\pages 175--204
\crossref{https://doi.org/10.1070/RM1976v031n04ABEH001564}


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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. Marc Artzrouni, “On the local stability of nonautonomous difference equations in n”, Journal of Mathematical Analysis and Applications, 122:2 (1987), 519  crossref
    2. P. N. Ivanshin, “Structure of function algebras on foliated manifolds”, Lobachevskii J. Math., 14 (2004), 39–54  mathnet  mathscinet  zmath  elib
    3. E. V. Gasnikova, “Dual multiplicative algorithms for an entropy-linear programming problem”, Comput. Math. Math. Phys., 49:3 (2009), 439–449  mathnet  crossref  mathscinet  isi  elib  elib
    4. Yinghua Fu, Qunfei Zhao, Lisheng Wang, “A converse to global exponential stability of a class of difference equations”, Adv Diff Equ, 2013:1 (2013), 9  crossref
    5. Cheban D., “Belitskii-Lyubich Conjecture For C-Analytic Dynamical Systems”, Discrete Contin. Dyn. Syst.-Ser. B, 20:3, SI (2015), 945–959  crossref  isi
    6. S. Kobzash, “Nepodvizhnye tochki i polnota v metricheskikh i obobschennykh metricheskikh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 127–215  mathnet
  • Успехи математических наук Russian Mathematical Surveys
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