Hermite–Hadamard-type inequalities via different convexities with applications

Abstract

Abstract In this paper, we explore a class of Hermite–Hadamard integral inequalities for convex and m-convex functions. The Hölder inequality is used to create this class, which has a wide range of applications in optimization theory. Some trapezoid-type inequalities and midpoint error estimates are investigated. Inequalities for several q-special functions are highlighted. As particular cases, we have included several previous results.

Keywords

• Error estimates
• Hermite–Hadamard-type inequalities
• m-convex function
• Trapezoid rule