Abstract

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.

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Keywords

  • Jessen's inequality
  • discrete and integral Jensen's inequalities
  • subadditive functionals
  • means

Mathematics Subject Classification

39B62, 26A51, 26D15

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Suggested citation

L. Horváth. “A Combinatorial Refinement of Generalized Jessen's Inequality.” Journal of Convex Analysis 29 (2022), No. 1, 61–76. https://doi.org/10.68381/jca29003

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.