On Hermite-Hadamard Type Integral Inequalities for Functions Whose Second Derivative are nonconvex

Mehmet Zeki SARIKAYAa,* Hakan Bozkurt and Mehmet Ey¨up KIRIS b

On Hermite-Hadamard Type Integral Inequalities for Functions Whose Second Derivative are nonconvex

Authors :

Mehmet Zeki SARIKAYA^a,* Hakan Bozkurt and Mehmet Ey¨up KIRIS^b

Author Address :

^aDepartment of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce-TURKEY.
^bDepartment of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University, Afyon-TURKEY.

*Corresponding author.

Abstract :

In this paper, we extend some estimates of the right hand side of a Hermite-Hadamard type inequality for nonconvex functions whose second derivatives absolute values are $varphi $-convex, log-$varphi $-convex, and quasi-$ varphi $-convex.

Keywords :

Hermite-Hadamard’s inequalities, $varphi $-convex functions, log-$ varphi $-convex, quasi-$varphi $-convex, H"{o}lder’s inequality.

DOI :

Article Info :

Received : December 03, 2013; Accepted : April 15, 2014.