Geodesic
Characterizing quasiconvex functions in terms of the Kronrod's tree of a~function
Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 777-780

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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
Mots-clés : quasiconvex functions. 
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     author = {A. I. Vorob'ev},
     title = {Characterizing quasiconvex functions in terms of the {Kronrod's} tree of a~function},
     journal = {Sbornik. Mathematics},
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A. I. Vorob'ev. Characterizing quasiconvex functions in terms of the Kronrod's tree of a~function. Sbornik. Mathematics, Tome 205 (2014) no. 6, pp. 777-780. http://geodesic.mathdoc.fr/item/SM_2014_205_6_a1/