Hermite-Hadamard type inequalities for quasi-convex functions via improved power-mean inequality

Abstract

In this paper, by using power-mean and improved power-mean integral inequality and an general identity for differentiable functions we can get new estimates on integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained improved power-mean integral inequality is better than the result obtained power-mean inequality. Some applications to special means of real numbers are also given.