Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second (q^{b}) -derivatives

摘要

In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of $q^{b}$ -integral. We prove some new inequalities related with right-hand sides of $q^{b}$ -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.