More Accurate Majorization Inequalities Obtained Via Superquadraticity and Convexity with Application to Entropies

Bradanovic, Slavica İvelic

doi:10.1007/s00009-021-01708-6

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…It remains to state more suitable forms of relations (10) and (11). More precisely, considering Theorem 3 with −ν instead of ν, we obtain appropriate external forms of (3).…”

Section: Our Next Intention Is To Derive An External Version Of the R...mentioning

confidence: 99%

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On logarithmically superquadratic functions

Krnić

Moradi

Sababheh

2023

Preprint

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In this paper, we develop a concept of a logarithmically super\-qua\-dratic function. Such a class of functions is defined via superquadratic functions.These functions possess some superior properties, especially if they take values greater than or equal to one. We prove that they are convex and superadditive in the latter case.In particular, we also obtain the corresponding refinement of the Jensen inequality in a product form. Furthermore, we derive an external form of the Jenseninequality and the corresponding reverse. Finally, we give a variant of the Jensen operator inequality for logarithmically superquadratic functions.All established results are derived via the corresponding relations for superquadratic functions.

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“…It remains to state more suitable forms of relations (10) and (11). More precisely, considering Theorem 3 with −ν instead of ν, we obtain appropriate external forms of (3).…”

Section: Our Next Intention Is To Derive An External Version Of the R...mentioning

confidence: 99%

“…For more details about superquadratic functions, including various examples, properties, and diverse applications in the theory of inequalities, the reader is referred to [2,3,6,7,8,10,18,21] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

On logarithmically superquadratic functions

Krnić

Moradi

Sababheh

2023

Preprint

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“…Moreover, the generalized results of majorization have been devoted to applications in information theory. In 2021, Bradanović [46] obtained some improvements of majorization inequalities with the help of superquadratic functions, which is in fact the generalized concept of convexity. The results are also associated with different entropies.…”

Section: Introductionmentioning

confidence: 99%

Improvements of Integral Majorization Inequality with Applications to Divergences

Basir,

Khan,

Ullah

et al. 2023

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Within the recent wave of research advancements, mathematical inequalities and their practical applications play a notably significant role across various domains. In this regard, inequalities offer a captivating arena for scholarly endeavors and investigational pursuits. This research work aims to present new improvements for the integral majorization inequalities using an interesting aproach. Certain previous improvements have been achieved for the Jensen inequality as direct outcomes of the main results. Additionally, estimates for the Csiszár divergence and its cases are provided as applications of the main results. The circumstances under which the principal outcomes offer enhanced estimations for majorization differences are also underscored and emphasized.

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Integral inequalities of h‐superquadratic functions and their fractional perspective with applications

Butt,

Khan

2024

Math Methods in App Sciences

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The purpose of this article is to provide a number of Hermite–Hadamard and Fejér type integral inequalities for a class of ‐superquadratic functions. We then develop the fractional perspective of inequalities of Hermite–Hadamard and Fejér types by use of the Riemann–Liouville fractional integral operators and bring up with few particular cases. Numerical estimations based on specific relevant cases and graphical representations validate the results. Another motivating component of the study is that it is enriched with applications of modified Bessel function of first type, special means, and moment of random variables by defining some new functions in terms of modified Bessel function and considering uniform probability density function. The results in this paper have not been initiated before in the frame of ‐superquadraticity. We are optimistic that this effort will greatly stimulate and encourage additional research.

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More Accurate Majorization Inequalities Obtained Via Superquadraticity and Convexity with Application to Entropies

Cited by 7 publications

References 12 publications

On logarithmically superquadratic functions

On logarithmically superquadratic functions

Improvements of Integral Majorization Inequality with Applications to Divergences

Integral inequalities of h‐superquadratic functions and their fractional perspective with applications

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