International Journal of Pure and Applied Mathematics Volume 80 No. 5 2012, 673-681 ISSN: 1311-8080 (printed version) url: http://www.ijpam.eu P A ijpam.eu REFINEMENTS OF HADAMARD TYPE INEQUALITIES FOR (α, 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 qth (q ≥ 1) power are (α, m)- convex.Some applications to special means of positive real numbers are consid- ered. AMS Subject Classification: 26D10, 39B62 Key Words: Hermite-Hadamard inequality, (α, m)-convex function, convex- ity, H¨ older inequality 1. Introduction Let f : I ⊆ R −→ R be a convex function on the interval I of real numbers and a, b ∈ I with a < b. Then we have the following double inequality, which is well known as the Hermite-Hadamard inequality f  a + b 2  ≤ 1 b − a  b a f (x)dx ≤ f (a)+ f (b) 2 . In 1993 [3], V. Mihesan introduced the class of (α, m)-convex functions as the following: Received: July 9, 2012 c  2012 Academic Publications, Ltd. url: www.acadpubl.eu