RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 171–190 (Mi izv4109)  

This article is cited in 4 scientific papers (total in 4 papers)

Stability of cascade search

T. N. Fomenko

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We find sufficient conditions on a searching multi-cascade for a modification of the set of limit points of the cascade that satisfy an assessing inequality for the distance from each of these points to the initial point to be small, provided that the modifications of the initial point and the initial set-valued functionals or maps used to construct the multi-cascade are small. Using this result, we prove the stability (in the above sense) of the cascade search for the set of common pre-images of a closed subspace under the action of $n$ set-valued maps, $n\ge1$ (in particular, for the set of common roots of these maps and for the set of their coincidences). For $n=2$ we obtain generalizations of some results of A. V. Arutyunov; the very statement of the problem comes from a recent paper of his devoted to the study of the stability of the subset of coincidences of a Lipschitz map and a covering map.

Keywords: multi-cascade, stability of cascade search, set-valued map, coincidence of $n$ maps.

DOI: https://doi.org/10.4213/im4109

Full text: PDF file (515 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:5, 1051–1068

Bibliographic databases:

UDC: 517.9
MSC: Primary 54H25; Secondary 47H10, 54C60, 54E40, 54H20, 58C06
Received: 23.04.2009
Revised: 29.06.2009

Citation: T. N. Fomenko, “Stability of cascade search”, Izv. RAN. Ser. Mat., 74:5 (2010), 171–190; Izv. Math., 74:5 (2010), 1051–1068

Citation in format AMSBIB
\Bibitem{Fom10}
\by T.~N.~Fomenko
\paper Stability of cascade search
\jour Izv. RAN. Ser. Mat.
\yr 2010
\vol 74
\issue 5
\pages 171--190
\mathnet{http://mi.mathnet.ru/izv4109}
\crossref{https://doi.org/10.4213/im4109}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2757904}
\zmath{https://zbmath.org/?q=an:1210.54052}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010IzMat..74.1051F}
\elib{http://elibrary.ru/item.asp?id=20358765}
\transl
\jour Izv. Math.
\yr 2010
\vol 74
\issue 5
\pages 1051--1068
\crossref{https://doi.org/10.1070/IM2010v074n05ABEH002515}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000285022600005}
\elib{http://elibrary.ru/item.asp?id=16979899}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78049326579}


Linking options:
  • http://mi.mathnet.ru/eng/izv4109
  • https://doi.org/10.4213/im4109
  • http://mi.mathnet.ru/eng/izv/v74/i5/p171

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. T. N. Fomenko, “Cascade Search for Preimages and Coincidences: Global and Local Versions”, Math. Notes, 93:1 (2013), 172–186  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. T. N. Fomenko, “Functionals strictly subjected to convergent series and search for singularities of mappings”, J. Fixed Point Theory Appl., 14:1 (2013), 21–40  crossref  mathscinet  zmath  isi  scopus
    3. S. R. Gajnullova, T. N. Fomenko, “Functionals Subordinate to Converging Series and Some Applications”, Math. Notes, 96:2 (2014), 294–297  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Fomenko T. Podoprikhin D., “On Preservation of Common Fixed Points and Coincidences Under a Homotopy of Mapping Families of Ordered Sets”, J. Optim. Theory Appl., 180:1, SI (2019), 34–47  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:316
    Full text:65
    References:44
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019