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    Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional integrals
    (Springer, 2021) You, Xue-Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Agarwal, Praveen; Chu, Yu-Ming
    In the paper, the authors establish some new Hermite-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite-Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.
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    New quantum boundaries for quantum Simpson's and quantum Newton's type inequalities for preinvex functions
    (Springer, 2021) Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hüseyin; Agarwal, Praveen; Murtaza, Ghulam; Chu, Yu-Ming
    In this research, we derive two generalized integral identities involving the q kappa 2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson's and quantum Newton's inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson's and Newton's type inequalities by considering the limit q -> 1- in the key results of this paper.
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    Some New Hermite-Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
    (Mdpi, 2021) Vivas-Cortez, Miguel; Ali, Muhammad Aamir; Budak, Hüseyin; Kalsoom, Humaira; Agarwal, Praveen
    In this investigation, for convex functions, some new (p,q)-Hermite-Hadamard-type inequalities using the notions of (p,q)(pi 2) derivative and (p,q)(pi 2) integral are obtained. Furthermore, for (p,q)(pi 2)-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)(pi 2) integral are offered. It is also shown that the newly proved results for p=1 and q -> 1(-) can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.