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Sbornik: Mathematics, 2014, Volume 205, Issue 6, Pages 777–780
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004398 (Mi sm8278) 		 
Characterizing quasiconvex functions in terms of the Kronrod's tree of a function

A. I. Vorob'ev
English version PDF (351 kB) Russian version article
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DOI: https://doi.org/10.1070/SM2014v205n06ABEH004398
Abstract: As an application of Kronrod's construction of the tree of a function to convex analysis, a characterization of quasiconvex functions is obtained. Namely, a function is quasiconvex if and only if the associated function defined on the tree of the original function is quasiconvex. A new proof of one of the existence lemmas in Kronrod's construction of the tree of a function (the original proof of which turned out to be incorrect) is given.
Bibliography: 4 titles.
Keywords: Kronrod's tree of a function, quasiconvex functions.
Received: 14.08.2013 and 14.01.2014
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 26B25, 46N10
Language: English
Original paper language: Russian
Citation: A. I. Vorob'ev, “Characterizing quasiconvex functions in terms of the Kronrod's tree of a function”, Sb. Math., 205:6 (2014), 777–780
Citation in format AMSBIB
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\paper Characterizing quasiconvex functions in terms of the Kronrod's tree of a~function
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\vol 205
\issue 6
\pages 777--780
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