Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

Lei, Hui; Hu, Gou; Cao, Zhijie; Du, Tingsong

doi:10.1186/s13660-019-2216-2

Cited by 3 publications

(1 citation statement)

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“…Mubeen [10] and Sarikaya and Karaca [11] introduced the notion of δ-fractional integrals. Using the concepts of δ-fractional calculus, Lei et al [12] obtained Hadamard δ-fractional inequalities of Fejer type using GA-s-convex functions. Luo et al [13] obtained bounds related to multiparameterized δ-fractional integrals and discussed their applications as well.…”

Section: Introductionmentioning

confidence: 99%

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

Akhtar

Awan

2021

Journal of Mathematics

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Section: Introductionmentioning

confidence: 99%

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

Akhtar

Awan

2021

Journal of Mathematics

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A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Tariq

Ntouyas

Shaikh

2023

Axioms

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A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented. In the numerous families of convexities, it includes classical convex functions, s-convex functions, quasi-convex functions, strongly convex functions, harmonically convex functions, harmonically quasi-convex functions, quasi-geometrically convex functions, p-convex functions, convexity with respect to strictly monotone function, co-ordinated-convex functions, (θ,h−m)−p-convex functions, and h-preinvex functions. Included in the fractional integral operators are Riemann–Liouville fractional integral, (k−p)-Riemann–Liouville, k-Riemann–Liouville fractional integral, Riemann–Liouville fractional integrals with respect to another function, the weighted fractional integrals of a function with respect to another function, fractional integral operators with the exponential kernel, Hadamard fractional integral, Raina fractional integral operator, conformable integrals, non-conformable fractional integral, and Katugampola fractional integral. Finally, Fejér-type fractional integral inequalities for invex functions and (p,q)-calculus are also included.

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Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

Vivas-Cortez

Awan

Talib

et al. 2022

MATH

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<abstract><p>The main objective of this paper is to derive some new variants of trapezium like inequalities involving $ k $-fractional integrals with exponential kernel essentially using the definition of preinvex functions. Fractional bounds associated with some new fractional integral identities are also obtained. In order to show the significance of our main results, we also discuss applications to means and $ q $-digamma functions. We discuss special cases which show that our results are quite unifying.</p></abstract>

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Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

Cited by 3 publications

References 24 publications

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

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Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

Cited by 3 publications

References 24 publications

Some δ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

Some δ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

Contact Info

Product

Resources

About

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

Some $δ$ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications