Post-quantum trapezoid type inequalities

Abstract

In this study, the assumption of being differentiable for the convex function f in the (p, q)-Hermite-Hadamard inequality is removed. A new identity for the right-hand part of (p, q)-Hermite-Hadamard inequality is proved. By using established identity, some (p, q)-trapezoid integral inequalities for convex and quasi-convex functions are obtained. The presented results in this work extend some results from the earlier research.

Keywords

• hermite-hadamard inequality
• <i>q</i>-integral inequalities
• (<i>p</i>
• <i>q</i>)-integral inequalities
• <i>q</i>)-derivative
• <i>q</i>)-integration
• convexity
• quasi-convexity