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Eurasian Math. J., 2015, Volume 6, Number 4, Pages 44–58 (Mi emj209)  

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

Invertibility of multivalued sublinear operators

I. V. Orlovab, S. I. Smirnovaa

a Department of Mathematics and Informatics, Crimean Federal V. Vernadsky University, 4 Academician Vernadsky Avenue, Simferopol, Republic Crimea, Russia, 295007
b Voronezh State University, 1 University Square, Voronezh, Russia, 394006

Abstract: We consider the representation of a compact-valued sublinear operator ($K$-operator) by means of the compact convex packet of single-valued so-called basis selectors. Such representation makes it possible to introduce the concept of an invertible $K$-operator via invertible selectors. The extremal points of direct and inverse selector representations are described, an analogue of the von Neumann theorem is obtained. A series of examples is considered.

Keywords and phrases: sublinear multivalued operators, basis selectors, Hamel basis, extremal points.

Funding Agency Grant Number
Russian Science Foundation 14-21-00066


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Document Type: Article
MSC: 47H04, 54C65, 46B22, 49N45, 47N10.
Received: 11.10.2015
Language: English

Citation: I. V. Orlov, S. I. Smirnova, “Invertibility of multivalued sublinear operators”, Eurasian Math. J., 6:4 (2015), 44–58

Citation in format AMSBIB
\Bibitem{OrlSmi15}
\by I.~V.~Orlov, S.~I.~Smirnova
\paper Invertibility of multivalued sublinear operators
\jour Eurasian Math. J.
\yr 2015
\vol 6
\issue 4
\pages 44--58
\mathnet{http://mi.mathnet.ru/emj209}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380173800004}


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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. I. V. Orlov, “Subdifferentials via sub-operators”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 235–238  isi
    2. S. Smirnova, I. Orlov, “Sublinear operator by basis selectors packet and sub-invertibility”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 295–298  isi
    3. F. S. Stonyakin, “An analogue of the Hahn–Banach theorem for functionals on abstract convex cones”, Eurasian Math. J., 7:3 (2016), 89–99  mathnet  mathscinet
    4. I. V. Orlov, “The Method of Lagrange Multipliers for the Class of Subsmooth Mappings”, Math. Notes, 103:2 (2018), 323–327  mathnet  crossref  crossref  isi  elib
  • Eurasian Mathematical Journal
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