Generalizations of Sherman’s inequality

Bradanovic, Slavica İvelic; Pečarić, Josip

doi:10.1007/s10998-016-0154-z

Cited by 9 publications

(2 citation statements)

References 4 publications

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“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”

Section: ) We Get Majorization Inequalitymentioning

confidence: 99%

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Bradanovic¹

2019

Turk J Math

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Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n -strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f -divergence and derived some reverse relations for such concept.

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“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”

Section: ) We Get Majorization Inequalitymentioning

confidence: 99%

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Bradanovic¹

2019

Turk J Math

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“…See [1,2,3,7,9,10,14,15,16] for some applications and generalizations of Sherman's inequality (1.6). Statement (1.5) is called Sherman's condition.…”

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confidence: 99%

A note on majorization properties of the Lieb function

Niezgoda

2020

ELA

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In this note, the Lieb function $(A,B) \to \Phi (A,B) = \tr \exp ( A + \log B )$ for an Hermitian matrix $A$ and a positive definite matrix $B$ is studied. It is shown that $\Phi$ satisfies a majorization property of Sherman type induced by a doubly stochastic operator. The variant for commuting matrices is also considered. An interpretation is given for the case of the orthoprojection operator onto the space of block diagonal matrices.

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A Note on the Positivity of the Even Degree Complete Homogeneous Symmetric Polynomials

Rovenţa

Temereancă

2018

Mediterr. J. Math.

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Generalizations of Sherman’s inequality

Cited by 9 publications

References 4 publications

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

A note on majorization properties of the Lieb function

A Note on the Positivity of the Even Degree Complete Homogeneous Symmetric Polynomials

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