Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators

Set, Erhan; Choi, Junesang; Alan, E. Aykan

doi:10.1007/s41478-018-0159-5

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Remark 3.9. The case a = 0 and α = 1 in Lemma 3.1, Theorem 3.2, Lemma 3.3, Theorem 3.4, Theorem 3.5, Theorem 3.6 and Theorem 3.7 reduces to the known results, respectively, in [11,Corollary 1], [11,Corollary 2], [11,Corollary 3], [11,Corollary 4], [11,Corollary 5], [11,Corollary 6] and [11,Corollary 7].…”

Section: Hermite-hadamard-fejér Type Inequalitiesmentioning

confidence: 83%

Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities involving fractional integral operators

Set

Ocak

Aykan

2019

Filomat

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Since the so-called Hermite-Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite-Hadamard inequalities and Hermite-Hadamard-Fejer type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the fractional conformable integral operators initiated by Jarad et al. [9]. We also point out that certain known inequalities are particular cases of the results presented here.

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Section: Hermite-hadamard-fejér Type Inequalitiesmentioning

confidence: 83%

Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities involving fractional integral operators

Set

Ocak

Aykan

2019

Filomat

Self Cite

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“…Aljaaidi with Pachpatte [3], presented Minkowski inequalities by mean of ψ-Riemann Liouville fractional integral operators. A large variety of inequalities have been proposed and studied for different fractional operators, see [11,31,35,36] and the references therein. In last few decades, a number of mathematician have devoted their efforts to generalize, extends and give numerous variants of the inequalities associated with the names of Minkowski, Hölder's, Hardy, Trapezoid, Ostrowski, Čebyšev, for more details, see [25,28].…”

Section: Introductionmentioning

confidence: 99%

$\pmbψ$-Caputo Fractional Iyengar's Type Inequalities

Yewale¹,

Pachpatte²

2020

Preprint

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In this paper, we establish Iyengar type inequalities utilizing ψ-Caputo fractional derivatives that is, fractional derivative of a function with respect to another function, which is generalization of some known fractional derivatives such as Riemann-Liouville, Hadamard, Erdélyi-Kober. The inequalities in this article are with respect to L p norms, 1 ≤ p ≤ ∞. The tools used in the analysis are based on Taylor's formulae for ψ-Caputo fractional derivatives.

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New integral inequalities of Hermite–Hadamard type via the Katugampola fractional integrals for strongly $$\eta$$-quasiconvex functions

Kermausuor

Nwaeze

2020

J Anal

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Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators

Cited by 3 publications

References 17 publications

Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities involving fractional integral operators

Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities involving fractional integral operators

$\pmbψ$-Caputo Fractional Iyengar's Type Inequalities

New integral inequalities of Hermite–Hadamard type via the Katugampola fractional integrals for strongly $$\eta$$-quasiconvex functions

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