• Korean Journal of Mathematics
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• 제26권3호
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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.

• Kyungpook Mathematical Journal
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• 제52권4호
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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.