摘要：AbstractIn this paper, we prove the correctq-Hermite–Hadamard inequality, some newq-Hermite–Hadamard inequalities, and generalizedq-Hermite–Hadamard inequality. By using the left hand part of the correctq-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give someq-midpoint type integral inequalities throughq-differentiable convex andq-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works.
关键词：Hermite–Hadamard inequality;Midpoint type inequality;q;-Integral inequalities;q;-Derivative;q;-Integration;Convexity;Quasi-convexity
