IJPAM: Volume 80, No. 5 (2012)

REFINEMENTS OF HADAMARD TYPE INEQUALITIES
FOR $(\alpha ,m)$-CONVEX FUNCTIONS

Noha Eftekhari
Faculty of Mathemathical Sciences
Shahrekord University
P.O. Box 115, Shahrekord, IRAN


Abstract. The aim of this work is to establish several new results related to the left hand side of the Hermite-Hadamard inequality for functions whose first derivative in absolute value aroused to the $q$th $(q\geq 1)$ power are $(\alpha ,m)$-convex.Some applications to special means of positive real numbers are considered.

Received: July 9, 2012

AMS Subject Classification: 26D10, 39B62

Key Words and Phrases: Hermite-Hadamard inequality, $(\alpha ,m)$-convex function, convexity, Hölder inequality

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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: 5