Some k-fractional associates of Hermite-Hadamard's inequality for quasi-convex functions and applications to special means

Hussain, Rashida; Ali, Asad; Latif, A.; Gulshan, Ghazala

doi:10.7153/fdc-2017-07-13

Cited by 14 publications

(16 citation statements)

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“…There are many applications to demonstrate the use of integral inequalities, especially applications on special means of the real numbers [2,5,8,39]. In this section, we present some examples to demonstrate the applications of our proposed results on modified Bessel functions and q-digamma functions.…”

Section: Examplesmentioning

confidence: 96%

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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Section: Examplesmentioning

confidence: 96%

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

2020

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“…Thus the class of quasiconvex functions contains the class of finite convex functions defined on finite closed intervals. The investigation of Hadamard inequality for quasiconvex functions is an implicit topic, and related results have been obtained independently by various authors; see, for example, [5,11,12] and references therein.…”

Section: Definition 8 ([12]mentioning

confidence: 99%

On boundedness of unified integral operators for quasiconvex functions

et al. 2020

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This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish bounds of these integral operators. We prove their boundedness and continuity. The results of this paper generalize already published results and have direct consequences for fractional and conformable integrals

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“…Definition 2 (See, e.g., [14], p. 302) Let I be an interval of real numbers. Then a function f : I → R is said to be quasi-convex function, if for all a, b ∈ I and 0 ≤ t ≤ 1 the following inequality holds:…”

Section: Introductionmentioning

confidence: 99%

“…( 1 ) Therefore it is noted that the class of quasi-convex functions contains the class of finite convex functions defined on finite closed intervals. The Hadamard and Hadamardtype inequalities for quasi-convex functions have been studied by many researchers (see [14,15,28] and the references therein). For more fractional inequalities of Hadamard and Hadamard-type we suggest references [1,2,8,[10][11][12][13]21].…”

Section: Introductionmentioning

confidence: 99%

Generalized fractional inequalities for quasi-convex functions

et al. 2019

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The class of quasi-convex functions contain all those finite convex functions which are defined on finite closed intervals of real line. The aim of this paper is to establish the bounds of the sum of left and right fractional integral operators using quasi-convex functions. An identity is formulated which is used to find Hadamard-type inequalities for quasi-convex functions. Connections with some known results are analyzed. Furthermore, some implications are derived by considering some examples of quasi-convex functions.

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Some k-fractional associates of Hermite-Hadamard's inequality for quasi-convex functions and applications to special means

Abstract: This article brings together some inequalities associated with Hermite-Hadamard's inequality for quasi-convex functions by way of k -Riemann-Liouville fractional integrals of order α . The inequalities thus obtained are applied to some special means of real numbers.

Cited by 14 publications

References 1 publication

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

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

On boundedness of unified integral operators for quasiconvex functions

Generalized fractional inequalities for quasi-convex functions

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