Integral inequalities in q-calculus

AbstractIn this paper, q-calculus analogues of some classical and some recent integral inequalities are found. Applications to estimation of sums of some convergent series are also given

(p, q)-Hermite-Hadamard inequalities and (p, q)-estimates for midpoint type inequalities via convex and quasi-convex functions

iscan, imdat/0000-0001-6749-0591; Kunt, Mehmet/0000-0002-8730-5370WOS: 000445335600005In this paper, we prove the correct (p, q)-Hermite-Hadamard inequality, some new (p, q)-Hermite-Hadamard inequalities, and generalized (p, q)-Hermite-Hadamard inequality. By using the left hand part of the correct (p, q)-Hermite-Hadamard inequality, we have a new equality. Finally using the new equality, we give some (p, q)-midpoint type integral inequalities through (p, q)-differentiable convex and (p, q)-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works