Jensen inequalities for P-class functions

Rooin, Jamal; Habibzadeh, S.; Moslehian, Mohammad Sal

doi:10.1007/s10998-017-0232-x

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…Lemma 2.3 can be applied to derive variants of (3.1) for MN-convex functions. See [1,12,15,16,18,21] and references therein for a collection of such inequalities.…”

Section: Matrix Jensen Inequalitymentioning

confidence: 99%

How type of Convexity of the Core function affects the Csiszár $f$-divergence functional

Kian¹

2021

Preprint

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We investigate how the type of Convexity of the Core function affects the Csiszár f -divergence functional. A general treatment for the type of convexity has been considered and the associated perspective functions have been studied. In particular, it has been shown that when the core function is MN-convex, then the associated perspective function is jointly MN-convex if the two scalar mean M and N are the same. In the case where M = N, we study the type of convexity of the perspective function. As an application, we prove that the Hellinger distance is jointly GG-convex. As further applications, the matrix Jensen inequality has been developed for the perspective functions under different kinds of convexity.

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“…Lemma 2.3 can be applied to derive variants of (3.1) for MN-convex functions. See [1,12,15,16,18,21] and references therein for a collection of such inequalities.…”

Section: Matrix Jensen Inequalitymentioning

confidence: 99%

How type of Convexity of the Core function affects the Csiszár $f$-divergence functional

Kian¹

2021

Preprint

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“…Bakula and Nikodem 31 presented counterparts and converses of the Jensen inequality by applying strongly convex functions while taking linear positive normalized functionals. Rooin et al 32 utilized P–class of convex functions and established an operator version of Jensen's inequality for normal operators. In 2021, Deng et al 33 acquired some interesting refinements of the Jensen inequality with the help of majorization theory.…”

Section: Introductionmentioning

confidence: 99%

Some estimations of the Jensen difference and applications

Khan

Ullah

Saeed

2022

Math Methods in App Sciences

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The Jensen inequality is one of the most favorable inequalities during the last few decades due to its expressive characteristics and properties. This inequality has gained a very dominant position in the several fields of science as a result of its extensive applications. In the present note, we use an interesting approach for the determination of estimates for the Jensen difference. We acquire several estimates for the Jensen difference while utilizing the convex function definition, Jensen's inequality for concave functions, power mean, and Hölder inequalities. For the real visualizations of the acquired estimates, we provide some particular examples. We get different improvements for the Hölder inequality while taking specified functions in the received estimates. Moreover, we deduce some more results from the main work in the form of improvements for the Hermite-Hadamard inequality. Furthermore, various relations for the famous quasi-arithmetic and power means are acquired with the help of established estimates. At the end, we present various applications of the main work in information theory. The intended applications provide some new bounds for the Csiszár and Rényi divergences, Shannon entropy, and Bhattacharyya co-efficient.

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