• Title/Summary/Keyword: f-Divergence measures

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INEQUALITIES FOR QUANTUM f-DIVERGENCE OF CONVEX FUNCTIONS AND MATRICES

  • Dragomir, Silvestru Sever
    • Korean Journal of Mathematics
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    • v.26 no.3
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    • pp.349-371
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    • 2018
  • Some inequalities for quantum f-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and ${\chi}^2-distance$ are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

  • Khan, Muhammad Adil;Khalid, Sadia;Pecaric, Josip
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.495-511
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    • 2012
  • In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.