Inequalities of Hermite–Hadamard type for functions whose derivatives in absolute value are convex with applications

Abstract

In this paper some new Hadamard-type inequalities for functions whose derivatives in absolute values are convex are established. Some applications to special means of real numbers are given. Finally, we also give some applications of our obtained results to get new error bounds for the sum of the midpoint and trapezoidal formulae.

Keywords

• Hermite–Hadamard’s inequality
• Convex functions
• Hölder inequality
• Power-mean inequality
• Special means