Geodesic
A Combinatorial Refinement of Generalized Jessen's Inequality
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 61-76
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Jessen's inequality is the functional form of Jensen's inequality for convex functions defined on an interval of real numbers. It is studied by many authors, but not always in a correct form. Jessen's inequality has a nice generalization based on totally normalised sublinear functionals. A brief overview of this topic is presented. The main result of this paper is a combinatorial improvement of the generalized Jessen's inequality. There are only a few refinements even for Jessen's inequality, our result gives a new type of refinement in a more general context. As an application we introduce and study new means.
Classification : 39B62, 26A51, 26D15
Mots-clés : Jessen's inequality, discrete and integral Jensen's inequalities, subadditive functionals, means 
@article{JCA_2022_29_1_JCA_2022_29_1_a2,
     author = {L. Horv\'ath},
     title = {A {Combinatorial} {Refinement} of {Generalized} {Jessen's} {Inequality}},
     journal = {Journal of convex analysis},
     pages = {61--76},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a2/}
}
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L. Horváth. A Combinatorial Refinement of Generalized Jessen's Inequality. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 61-76. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a2/