Estimation-type results on the <i>k</i>-fractional Simpson-type integral inequalities and applications

Nie, Jialu; Liu, Jun; Zhang, Jiafeng; Du, Tingsong

doi:10.1080/16583655.2019.1663574

Cited by 4 publications

(2 citation statements)

References 20 publications

(14 reference statements)

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“…For example, Hu et al [23] obtained some new fractional analogues of integral inequalities using Katugampola fractional integrals. Nie et al [24] obtained k-fractional analogues of Simpson's inequality. Peng et al [25] also obtained some new fractional analogues of Simpson's inequality.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Chu

Awan

Javad

et al. 2020

Journal of Mathematics

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The goal of this paper is to derive some new variants of Simpson’s inequality using the class of n-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.

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Section: Introductionmentioning

confidence: 99%

Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Chu

Awan

Javad

et al. 2020

Journal of Mathematics

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“…One of the most studied results in this regard is Hermite-Hadamard's inequality. For some interesting details, see [8][9][10][11][12][13].…”

mentioning

confidence: 99%

Fractional Jensen-Mercer Type Inequalities Involving Generalized Raina’s Function and Applications

et al. 2022

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The aim of this paper is to derive some new generalized fractional analogues of Mercer type inequalities, essentially using the convexity property of the functions and Raina’s function. We also discuss several new special cases which show that our results are, to an extent, unifying. In order to illustrate the significance of our results, we offer some interesting applications of our results to special means, error bounds, and q-digamma functions.

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Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

Vivas-Cortez¹,

Awan²,

Javed³

et al. 2021

MATH

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<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

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Estimation-type results on the k-fractional Simpson-type integral inequalities and applications

Cited by 4 publications

References 20 publications

Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Fractional Jensen-Mercer Type Inequalities Involving Generalized Raina’s Function and Applications

Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

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