## HERMITE-HADAMARD TYPE INEQUALITIES FOR QUASI-CONVEX FUNCTIONS VIA IMPROVED POWER-MEAN INEQUALITY.

## HERMITE-HADAMARD TYPE INEQUALITIES FOR QUASI-CONVEX FUNCTIONS VIA IMPROVED POWER-MEAN INEQUALITY

*M. Kadakal*

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## Abstract

In this paper, by using power-mean and improved power-mean integral in- equality 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 ap- plications to special means of real numbers are also given.

## Keywords

Hermite-Hadamard inequality, improved power-mean inequality, midpoint type inequality, convex function, quasi-convex unctions.