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

Silvestru Sever Dragomir ()
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Silvestru Sever Dragomir: Victoria University

A chapter in Modern Discrete Mathematics and Analysis, 2018, pp 117-172 from Springer

Abstract: 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 χ 2 -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 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-74325-7_6

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DOI: 10.1007/978-3-319-74325-7_6

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