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Öğe Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional integrals(Springer, 2021) You, Xue-Xiao; Ali, Muhammad Aamir; Budak, Huseyin; Agarwal, Praveen; Chu, Yu-MingIn 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.Öğe A new generalization of some quantum integral inequalities for quantum differentiable convex functions(Springer, 2021) Li, Yi-Xia; Ali, Muhammad Aamir; Budak, Huseyin; Abbas, Mujahid; Chu, Yu-MingIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite-Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite-Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint-trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.Öğe New quantum boundaries for quantum Simpson's and quantum Newton's type inequalities for preinvex functions(Springer, 2021) Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Huseyin; Agarwal, Praveen; Murtaza, Ghulam; Chu, Yu-MingIn 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.Öğe On some new midpoint inequalities for the functions of two variables via quantum calculus(Springer, 2021) You, Xuexiao; Ali, Muhammad Aamir; Erden, Samet; Budak, Huseyin; Chu, Yu-MingIn this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the comparable consequences in the literature on the midpoint inequalities for differentiable coordinated convex mappings.Öğe Post-quantum Hermite-Hadamard type inequalities for interval-valued convex functions(Springer, 2021) Ali, Muhammad Aamir; Budak, Huseyin; Murtaza, Ghulam; Chu, Yu-MingIn this research, we introduce the notions of (p, q)-derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite-Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite-Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite-Hadamard inequalities.Öğe Quantum Hermite-Hadamard-type inequalities for functions with convex absolute values of second qb-derivatives(Springer, 2021) Ali, Muhammad Aamir; Budak, Huseyin; Abbas, Mujahid; Chu, Yu-MingIn this paper, we obtain Hermite-Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite-Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard inequalities.Öğe Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus(De Gruyter Poland Sp Z O O, 2021) Ali, Muhammad Aamir; Budak, Huseyin; Akkurt, Abdullah; Chu, Yu-MingIn this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of vertical bar(b)D(q)(2)f vertical bar and vertical bar(a)D(q)(2)f vertical bar, we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q(a) and q(b)-quantum integrals. The results presented here are the generalization of already published ones.Öğe Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables(Springer, 2021) Ali, Muhammad Aamir; Chu, Yu-Ming; Budak, Hueseyin; Akkurt, Abdullah; Yildirim, Hueseyin; Zahid, Manzoor AhmedIn this investigation, we demonstrate the quantum version of Montgomery identity for the functions of two variables. Then we use the result to derive some new Ostrowski-type inequalities for the functions of two variables via quantum integrals. We also consider the particular cases of the key results and offer some new integral inequalities.Öğe Refinements of quantum Hermite-Hadamard- type inequalities(De Gruyter Poland Sp Z O O, 2021) Budak, Huseyin; Khan, Sundas; Ali, Muhammad Aamir; Chu, Yu-MingIn 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.Öğe Weighted Hermite-Hadamard type inclusions for products of co-ordinated convex interval-valued functions(Springer, 2021) Kara, Hasan; Budak, Huseyin; Ali, Muhammad Aamir; Sarikaya, Mehmet Zeki; Chu, Yu-MingIn this paper, we establish some Hermite-Hadamard-Fejer type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earlier works.
