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Recent Developments of Discrete Inequalities for Convex Functions Defined on Linear Spaces with Applications

  • Silvestru Sever DragomirEmail author
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 131)

Abstract

In this paper we survey some recent discrete inequalities for functions defined on convex subsets of general linear spaces. Various refinements and reverses of Jensen’s discrete inequality are presented. The Slater inequality version for these functions is outlined. As applications, we establish several bounds for the mean f-deviation of an n-tuple of vectors as well as for the f-divergence of an n -tuple of vectors given a discrete probability distribution. Examples for the K. Pearson χ2-divergence, theKullback-Leibler divergence, the Jeffreys divergence, the total variation distance and other divergence measures are also provided.

Keywords

Convex functions on linear spaces Discrete Jensen’s inequality Reverse of Jensen’s inequality Discrete divergence measures f-Divergence measures 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics, College of Engineering & ScienceVictoria UniversityMelbourne CityAustralia
  2. 2.DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science & Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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