Estimates for Tsallis relative operator entropy

Moradi, Hamid Reza; Furuichi, Shigeru; Minculete, Nicuşor

doi:10.7153/mia-2017-20-69

Cited by 11 publications

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“…Several properties of divergences can be extended in the operator theory [22]. For the Tsallis divergence, we have the following relations.…”

Section: Resultsmentioning

confidence: 99%

Refined Young inequality and its application to divergences

Furuichi,

Minculete

2021

Preprint

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We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys-Tsallis divergence and the Jensen-Shannon-Tsallis divergence.

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“…Several properties of divergences can be extended in the operator theory [22]. For the Tsallis divergence, we have the following relations.…”

Section: Resultsmentioning

confidence: 99%

Refined Young inequality and its application to divergences

Furuichi,

Minculete

2021

Preprint

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“…We compare Theorem 2.6 and Theorem 2.2 in [16]. The inequalities k p (t) ≤ c p (t) ≤ l p (t) + (t−1) 2 4 given in (5) are equivalent to the following inequalities…”

Section: Remark 27mentioning

confidence: 99%

“…In [16], we obtained the estimates on Tsallis relative operator entropy by the use of Hermite-Hadamard inequality:…”

Section: Alternative Estimate Of Tsallis Relative Operator Entropymentioning

confidence: 99%

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Inequalities for Relative Operator Entropies and Operator Means

Furuichi

Minculete

2018

Acta Math Vietnam

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The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to derive these bounds, we established the significant relation between the Tsallis relative operator entropy and the generalized relative operator entropy. In addition, we study the properties on monotonicity for the weight of operator means, and for the parameter of relative operator entropies.Keywords : Operator inequality, positive operator, Hermite-Hadamard inequality, operator mean, generalized relative operator entropy and Tsallis relative operator entropy. Mathematics Subject Classification : 47A63, 47A64 and 94A17where we respectively denote p-weighted harmonic operator mean, p-weighted geometric operator mean and p-weighted arithmetic operator mean by A! p B ≡ (1 − p)A −1 + pB −1 −1 , A# p B ≡ A 1/2 A −1/2 BA −1/2 p A 1/2 and A∇ p B ≡ (1 − p)A + pB for A, B > 0 and p ∈ [0, 1].On the other hand, Tsallis defined the one-parameter extended entropy for the analysis of a physical model in statistical physics in [19]. The properties of the Tsallis relative entropy was studied in [6,7], by Furuichi, Yanagi and Kuriyama. The relative operator entropy S (A|B) := A 1/2 log A −1/

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“…The Jeffreys divergence (see [ 22 , 23 ]) is defined by

and the Jensen–Shannon divergence [ 15 , 16 ] is defined by

In [ 24 ], the Jeffreys and the Jensen–Shannon divergence are extended to biparametric forms. In [ 23 ], Furuichi and Mitroi generalizes these divergences to the Jeffreys–Tsallis divergence, which is given by

and to the Jensen–Shannon–Tsallis divergence, which is defined as

Several properties of divergences can be extended in the operator theory [ 25 ].…”

Section: Applications To Some Divergencesmentioning

confidence: 99%

Refined Young Inequality and Its Application to Divergences

Furuichi

Minculete

2021

Entropy

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We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys–Tsallis divergence and the Jensen–Shannon–Tsallis divergence.

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Estimates for Tsallis relative operator entropy

Cited by 11 publications

References 0 publications

Refined Young inequality and its application to divergences

Refined Young inequality and its application to divergences

Inequalities for Relative Operator Entropies and Operator Means

Refined Young Inequality and Its Application to Divergences

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