IJPAM: Volume 78, No. 5 (2012)

HERMITE AND SIMPSON-LIKE TYPE INEQUALITIES
FOR FUNCTIONS WHOSE SECOND DERIVATIVES
IN ABSOLUTE VALUES AT CERTAIN
POWERS ARE $s$-CONVEX

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


Abstract. In this article a general integral identity for twice differentiable mappings is derived. By using this result, the author establish some new Hermite-Hadamard-like type and Simpson-like type inequalities for twice differentiable $s$-convex mappings in the second sense.

Received: December 3, 2011

AMS Subject Classification: 26A51, 26B25, 26E15

Key Words and Phrases: $(\alpha,m)$-convexity, Simpson inequality, integral means

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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: 78
Issue: 5