
Journal of Convex Analysis 29 (2022), No. 1, 061076 Copyright Heldermann Verlag 2022 A Combinatorial Refinement of Generalized Jessen's Inequality László Horváth Dept. of Mathematics, University of Pannonia, Veszprém, Hungary lhorvath@almos.unipannon.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. [ Fulltextpdf (123 KB)] for subscribers only. 