The Hadamard Inequality For Convex Function Via Fractional Integrals

Özdemi̇r, M. Emi̇n; Ragomir, S.S.; Yıldız, Çetin

doi:10.1016/s0252-9602(13)60081-8

Cited by 46 publications

(18 citation statements)

References 6 publications

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“…Further, if we take , then we obtain Lemma 2.1 in [ 12 ]. In Corollary 2.2 , if we put , then we obtain Lemma 3 in [ 11 ], if we put and , then we obtain Lemma 2 in [ 8 ], if we put and , then we obtain Lemma 2.1 in [ 36 ]. …”

Section: A Lemmamentioning

confidence: 99%

k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappings

Wang

Yao

2017

J Inequal Appl

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Section: A Lemmamentioning

confidence: 99%

k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappings

Wang

Yao

2017

J Inequal Appl

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“…Authors of recent decades have studied the inequality (1.2), known as Hermite-Hadamard inequality (or trapezium inequality) in the premises of newly invented definitions due to motivation of convex function. Interested readers can see the references [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,29,30,31]. The stability theory for functional inequalities has its origin in the paper of Hyers and Ulam [13], in which the notion of δ-convex functions is introduced.…”

Section: Introductionmentioning

confidence: 99%

Some integral inequalities for approximately h—convex functions and their applications

Kashuri

Raees

Anwar

2021

Proyecciones (Antofagasta)

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In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given.

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“…The subject of the fractional calculus (integrals and derivatives) is a popular topic due to its fundamental applications in dealing with the dynamics of the complex sytems. This subject is still being studied extensively by many authors, see, for instance, [3,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

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.

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The Hadamard Inequality For Convex Function Via Fractional Integrals

Cited by 46 publications

References 6 publications

k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappings

k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappings

Some integral inequalities for approximately h—convex functions and their applications

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

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