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arXiv · 1706.08047

Convexity of parameter extensions of some relative operator entropies with a perspective approach

Ismail Nikoufar
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Abstract

In this paper, we introduce two notions of a relative operator $(\alpha, \beta)$-entropy and a Tsallis relative operator $(\alpha, \beta)$-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative operator entropy. We apply a perspective approach to prove the joint convexity or concavity of these new notions, under certain conditions concerning $\alpha$ and $\beta$. Indeed, we give the parametric extensions, but in such a manner that they remain jointly convex or jointly concave.

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Ismail Nikoufar. 2017-06-25. Convexity of parameter extensions of some relative operator entropies with a perspective approach. https://arxiv.org/abs/1706.08047

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