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Hermite–Hadamard type inequalities for fractional integrals via Green’s function [PDF]

Journal of Inequalities and Applications, 2018
In the article, we establish the left Riemann–Liouville fractional Hermite–Hadamard type inequalities and the generalized Hermite–Hadamard type inequalities by using Green’s function and Jensen’s inequality, and present several new Hermite–Hadamard type ...
Muhammad Adil Khan, Arshad Iqbal, Muhammad Suleman, Yu-Ming Chu   +3 more
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Error Bound of Hermite–Hadamard–Mercer Inequalities via ψ−Conformable Fractional Integral Operators on the Coordinates

International Journal of Mathematics and Mathematical Sciences
This paper develops a family of Hermite–Hadamard–Mercer-type inequalities within the framework of generalized conformable fractional calculus. By interpreting generalized conformable fractional integrals as weighted integral means depending on the order ...
Jen Chieh Lo
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Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Mathematics, 2021
In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions.
Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Jiraporn Reunsumrit, Thanin Sitthiwirattham   +4 more
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Hermite-Hadamard-Fejér Inequalities for Preinvex Functions on Fractal Sets [PDF]

Sahand Communications in Mathematical Analysis, 2023
In this paper, for generalised preinvex functions, new estimates of the Fej\'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study.
Sikander Mehmood, Fiza Zafar
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Quantum Inequalities of Hermite–Hadamard Type for r-Convex Functions

Journal of Mathematics, 2021
In this present study, we first establish Hermite–Hadamard type inequalities for r-convex functions via qκ2-definite integrals. Then, we prove some quantum inequalities of Hermite–Hadamard type for product of two r-convex functions.
Xuexiao You, Hasan Kara, Hüseyin Budak, Humaira Kalsoom   +3 more
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Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second q b $q^{b}$ -derivatives

Advances in Difference Equations, 2021
In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of q b $q^{b}$ -integral. We prove some new inequalities related with right-hand sides of q b $q^{b}$ -Hermite–Hadamard inequalities for differentiable
Muhammad Aamir Ali, Hüseyin Budak, Mujahid Abbas, Yu-Ming Chu   +3 more
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Examining the Hermite–Hadamard Inequalities for k-Fractional Operators Using the Green Function

Fractal and Fractional, 2023
For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by
Çetin Yildiz, Luminiţa-Ioana Cotîrlă
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Refinements of quantum Hermite-Hadamard-type inequalities

Open Mathematics, 2021
In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.
Budak Hüseyin, Khan Sundas, Ali Muhammad Aamir, Chu Yu-Ming   +3 more
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Inequalities Pertaining Fractional Approach through Exponentially Convex Functions

Fractal and Fractional, 2019
In this article, certain Hermite-Hadamard-type inequalities are proven for an exponentially-convex function via Riemann-Liouville fractional integrals that generalize Hermite-Hadamard-type inequalities.
Saima Rashid, Muhammad Aslam Noor, Khalida Inayat Noor   +2 more
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Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

Journal of Inequalities and Applications, 2021
In this research, we introduce the notions of ( p , q ) $(p,q)$ -derivative and integral for interval-valued functions and discuss their fundamental properties.
Muhammad Aamir Ali, Hüseyin Budak, Ghulam Murtaza, Yu-Ming Chu   +3 more
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