On an upper bound for Sherman’s inequality

Bradanovic, Slavica İvelic; Latif, Naveed; Pečarić, Josip

doi:10.1186/s13660-016-1091-3

Cited by 5 publications

(2 citation statements)

References 3 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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“…The purpose of this paper is to extend Sherman's result to the more general class of n-convex functions and to give improvements of Sherman's inequality (1) from which extensions and improvements of Majorization inequality and Jensen's inequality immediately follow. Some related results can be found in [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Extensions and improvements of Sherman’s and related inequalities for n-convex functions

Bradanovic

Pečarić

2017

Open Mathematics

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This paper gives extensions and improvements of Sherman's inequality for n-convex functions obtained by using new identities which involve Green's functions and Fink's identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen's inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.

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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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On an upper bound for Sherman’s inequality

Cited by 5 publications

References 3 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

Extensions and improvements of Sherman’s and related inequalities for n-convex functions

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

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