Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals

Mehmood, Sikander; Zafar, Fiza; Yasmin, Nusrat

doi:10.3390/math7050467

Cited by 10 publications

(3 citation statements)

References 3 publications

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“…Due to broad utility of Hermite-Hadamard inequalities and fractional calculus, and across various scientific disciplines, researchers are actively exploring these type of inequalities. This research direction has gained momentum, as evidenced by recent developments in the field (see e.g., [12][13][14][15][16][17]). Sarikaya et al,in [18] established the Hermite-Hadamard type inequalities for fractional integrals:…”

Section: Definitionmentioning

confidence: 99%

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Mehmood,

Mohammed,

Kashuri

et al. 2024

Symmetry

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There is a strong correlation between the concept of convexity and symmetry. One of these is the class of interval-valued cr-log-h-convex functions, which is closely related to the theory of symmetry. In this paper, we obtain Hermite–Hadamard and its weighted version inequalities that are related to interval-valued cr-log-h-convex functions, and some known results are recaptured. To support our main results, we offer three examples and two applications related to modified Bessel functions and special means as well.

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Section: Definitionmentioning

confidence: 99%

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Mehmood,

Mohammed,

Kashuri

et al. 2024

Symmetry

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“…Recently, the following identity has been proved by Sikander et. al in [20] for ň−times differentiable preinvex functions.…”

Section: Introductionmentioning

confidence: 99%

On Fejér-Hermite-Hadamard inequalities for functions involving fractional integrals

Mehmood¹,

Zafar²,

Furkan³

et al. 2023

MMN

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In this paper, some new estimations of Hermite-Hadamard-Fejér type inequalities for higher order differentiable preinvex functions are established via fractional integral operators. The main motivation point of the study is that our findings, which include generalized preinvex functions for Hermite-Hadamard-Fejer type inequalities by means of fractional integral operators, are the rare results in the literature. The coincidence of the special cases of the our main theorems with the earlier works in the literature is also demonstrated as a verification of our results.

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“…where ω : [κ 1 ; κ 2 ] → is non-negative, integrable, and symmetric about τ = κ 1 +κ 2 2 . First, we mention some preliminary concepts and results that will be helpful in the sequel, for more details see [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

Kalsoom

Khan

2022

Mathematics

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In this work, we introduce new definitions of left and right-sides generalized conformable K-fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for ϕ-preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable K-fractional integrals regarding ϕ-preinvex functions. Finally, we also present some applications of the generalized definitions for higher moments of continuous random variables, special means, and solutions of the homogeneous linear Cauchy-Euler and homogeneous linear K-fractional differential equations to show our new approach.

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Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals

Cited by 10 publications

References 3 publications

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

Some New Fractional Inequalities Defined Using cr-Log-h-Convex Functions and Applications

On Fejér-Hermite-Hadamard inequalities for functions involving fractional integrals

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

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