2020
DOI: 10.1155/2020/4303727
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New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

Abstract: In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable func… Show more

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Cited by 13 publications
(3 citation statements)
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“…Remark 19. If we set ψ(c) � c in eorem 10, we obtain eorem 5 of [29]. Moreover, if we set ℓ 1 � y 1 and ℓ 2 � y 2 , we get eorem 5 of [32].…”
Section: Lemma 4 If (A 1 ) Is Satisfied and λmentioning
confidence: 99%
“…Remark 19. If we set ψ(c) � c in eorem 10, we obtain eorem 5 of [29]. Moreover, if we set ℓ 1 � y 1 and ℓ 2 � y 2 , we get eorem 5 of [32].…”
Section: Lemma 4 If (A 1 ) Is Satisfied and λmentioning
confidence: 99%
“…Transform theory, engineering, modeling, finance, mathematical biology, fluid flow, natural phenomenon prediction, healthcare, and image processing are all domains where fractional calculus is used. The references [1,10,11,24] provide further insights into this topic.…”
Section: Introductionmentioning
confidence: 99%
“…In [31], Butt et al presented the Hermite-Jensen-Mercer type inequalities for conformable fractional integrals within the year 2020. Furthermore, they developed the Hermite-Jensen-Mercer-like inequalities for k-fractional integrals, generalized fractional integrals and ψ-Riemann-Liouville k-fractional integrals (see [32][33][34]). In 2020, several researchers presented Hermite-Jensen-Mercer-like inequalities in the setting of a k-Caputo fractional derivative and Caputo fractional derivative (see [35,36]).…”
Section: Introductionmentioning
confidence: 99%