Jensen‐Grüss inequality and its applications for the Zipf‐Mandelbrot law

Butt, Saad Ihsan; Bakula, Milica Klaričić; Pec̆arić, Ðilda; Pečarić, Josip

doi:10.1002/mma.6869

Cited by 33 publications

(16 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, this inequality has been used in various areas of sciences and technology to solve several problems, such as engineering, mathematical statistics, financial economics, and computer science. Some recent results can be seen in [12][13][14].…”

Section: Definition 1 a Function λmentioning

confidence: 99%

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Butt

Umar²,

Khan

et al. 2021

Complexity

Self Cite

View full text Add to dashboard Cite

In this paper, authors prove new variants of Hermite–Jensen–Mercer type inequalities using ψ –Riemann–Liouville fractional integrals with respect to another function via convexity. We establish generalized identities involving ψ –Riemann–Liouville fractional integral pertaining first and twice differentiable convex function λ , and these will be used to derive novel estimates for some fractional Hermite–Jensen–Mercer type inequalities. Some known results are recaptured from our results as special cases. Finally, an application from our results using the modified Bessel function of the first kind is established as well.

show abstract

Section: Definition 1 a Function λmentioning

confidence: 99%

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Butt

Umar²,

Khan

et al. 2021

Complexity

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [29], the authors defined the weighted Caputo-Fabrizio fractional derivative and studied related linear and nonlinear fractional differential equations. In the literature, very little work has been reported on fractional integral inequalities using [33,34] proved some new integral inequalities by using generalized fractional integral operators and some classical inequalities for integrable functions and their applications to the Zipf-Mandelbrot law. Motivated by the above work, the main objective of this article is to establish some new results for the Pólya-Szegö inequality and some other inequalities using the Caputo-Fabrizio fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach

Nale

Chinchane²,

Panchal

et al. 2022

Axioms

View full text Add to dashboard Cite

show abstract

“…Jensen's inequality is the key to success in extracting applications in information theory. It is effective in finding estimates for several quantitative measures in information theory about continuous random variables, see [1][2][3]. The (J-I) can be stated as a generalization of convex functions as follows:…”

Section: Introductionmentioning

confidence: 99%

New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

Butt

Yousaf

Asghar

et al. 2021

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.

show abstract

Jensen‐Grüss inequality and its applications for the Zipf‐Mandelbrot law

Abstract: In this paper, we prove several Jensen‐Grüss type inequalities under various conditions. Some applications in information theory are also given.

Cited by 33 publications

References 6 publications

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to Another Function and Application

Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach

New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

Contact Info

Product

Resources

About