Geodesic
On Korenblum convex functions
Commentationes Mathematicae, Tome 57 (2017) no. 1, p. 25−44.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second \(\kappa\)-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the \(\kappa\)-convex functions.
DOI : 10.14708/cm.v57i1.1542
Classification : 39B62, 26B25, 26A48
Mots-clés : Convex function, \(\kappa\)-entropy, generalized convexity 
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Lorena Maria Lopez; Jurancy Ereú; Nelson Merentes. On Korenblum convex functions. Commentationes Mathematicae, Tome 57 (2017) no. 1, p.  25−44. doi : 10.14708/cm.v57i1.1542. http://geodesic.mathdoc.fr/articles/10.14708/cm.v57i1.1542/

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