Hermite‐Hadamard inequalities for Riemann‐Liouville fractional integrals of a convex function with respect to a monotone function

Mohammed, Pshtiwan Othman

doi:10.1002/mma.5784

Cited by 55 publications

(36 citation statements)

References 20 publications

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“…(see [15][16][17][18] for the fractional setting). Fractional calculus, one of the areas where inequality theory has benefited most in recent years, is an area that continues its development with a high acceleration by defining new fractional derivative and integral operators.…”

Section: Theorem 11 If ϒ Is a Convex Function Onmentioning

confidence: 99%

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

et al. 2020

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Section: Theorem 11 If ϒ Is a Convex Function Onmentioning

confidence: 99%

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

et al. 2020

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“…Meanwhile, they obtained some inequalities of midpoint type in the same paper. There are many papers studying integral inequalities for the Riemann-Liouville fractional integrals and some new relevant generalizations of Hermite-Hadamard type inequalities (see [11,12,19,[21][22][23][24][25][26][27] for more details).…”

Section: Introductionmentioning

confidence: 99%

A New Version of the Hermite–Hadamard Inequality for Riemann–Liouville Fractional Integrals

Mohammed

Brevik

2020

Symmetry

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Integral inequalities play a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods. Thus, the present days need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition. There is a strong relationship between convexity and symmetry. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the past few years. In this article, we firstly point out the known Hermite–Hadamard (HH) type inequalities which are related to our main findings. In view of these, we obtain a new inequality of Hermite–Hadamard type for Riemann–Liouville fractional integrals. In addition, we establish a few inequalities of Hermite–Hadamard type for the Riemann integrals and Riemann–Liouville fractional integrals. Finally, three examples are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

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“…One of the most important applications of fractional integrals is the well known inequality of the Hermite-Hadamard type, see [3,[7][8][9]11,[26][27][28][29][30][31][32][33][34] for more detail.…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals

2020

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Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of λ -incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite–Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann–Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

show abstract

Hermite‐Hadamard inequalities for Riemann‐Liouville fractional integrals of a convex function with respect to a monotone function

Cited by 55 publications

References 20 publications

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

A New Version of the Hermite–Hadamard Inequality for Riemann–Liouville Fractional Integrals

On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals

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