IJPAM: Volume 78, No. 5 (2012)

ON THE SIMPSON-LIKE TYPE INEQUALITIES FOR
TWICE DIFFERENTIABLE $(\alpha, m)$-CONVEX MAPPINGS

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


Abstract. In this article the author establish new results related to the Simpson-like inequalities for twice differentiable $(\alpha, m)$-convex mappings whose second derivatives in absolute values aroused to the $q$-th $(q\geq 1)$ power are $(\alpha, m)$-convex. Some applications to special means of positive real numbers are also given.

Received: January 12, 2012

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