IJPAM: Volume 80, No. 3 (2012)

HERMITE-HADAMARD-LIKE AND SIMPSON-LIKE TYPE
INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE
STRONGLY $\varphi$-CONVEX FUNCTIONS

Jaekeun Park
Department of Mathematics
Hanseo University
Seosan, Chungnam, 356-706, KOREA


Abstract. In this article, several inequalities of the Hermite-Hadamard-like and Simpson-like type integral inequalities are obtained for the class of functions whose second derivatives in absolute value at certain powers are strongly $\varphi$-convex with modulus $c>0.$

Received: August 8, 2012

AMS Subject Classification: 26D10, 26A51

Key Words and Phrases: Hermite-Hadamard inequality, Simpson's inequality, $\varphi$-convexity

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3