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

In: Modern Discrete Mathematics and Analysis

Author

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  • Silvestru Sever Dragomir

    (Victoria University
    University of the Witwatersrand)

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.

Suggested Citation

  • Silvestru Sever Dragomir, 2018. "Recent Developments of Discrete Inequalities for Convex Functions Defined on Linear Spaces with Applications," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Modern Discrete Mathematics and Analysis, pages 117-172, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-74325-7_6
    DOI: 10.1007/978-3-319-74325-7_6
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