Journal of Convex Analysis 29 (2022), No. 1, 061--076
Copyright Heldermann Verlag 2022
A Combinatorial Refinement of Generalized Jessen's Inequality
László Horváth
Dept. of Mathematics, University of Pannonia, Veszprém, Hungary
lhorvath@almos.uni-pannon.hu
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.
Keywords: Jessen's inequality, discrete and integral Jensen's inequalities, subadditive functionals, means.
MSC: 39B62, 26A51, 26D15.
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