On Hermite-Hadamard Type Integral Inequalities for Functions Whose Second Derivative are nonconvex
Authors :
Mehmet Zeki SARIKAYAa,* 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.