## IMPROVEMENTS ON SOME INEQUALITIES OF HERMITE HADAMARD INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE SECOND DERIVATIVE h AND P-CONVEX

## IMPROVEMENTS ON SOME INEQUALITIES OF HERMITE HADAMARD INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE SECOND DERIVATIVE h AND P-CONVEX

*E. Ünlüyol, S. Salaş, G. Dalkun*

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## Abstract

In this paper, firstly we obtain some improvements of Hermite-Hadamard integral inequalities via h and P-convex by using Ho ̈lder-I ̇ ̧scan inequality. Secondly new results are established. Thirdly, we determine some new inequalities for functions when a power of the absolute value of second derivatives are h and P-convex. Finally they are compared with the old ones.

## Keywords

Ho ̈lder-I ̇ ̧scan integral inequality, improved power-mean integral inequality, Her- mite Hadamard integral inequality, h and P -convexity.