International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 809689, 12 pages
http://dx.doi.org/10.1155/2012/809689
Research Article

Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable ( 𝛼 , 𝑚 )-Convex Mappings

Jaekeun Park

Department of Mathematics, Hanseo University, Chungnam-do, Seosan-si 356-706, Republic of Korea

Received 13 July 2011; Revised 13 November 2011; Accepted 28 November 2011

Academic Editor: Jewgeni Dshalalow

Copyright © 2012 Jaekeun Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The author establish several Hermite-Hadamard and Simpson-like type inequalities for mappings whose first derivative in absolute value aroused to the 𝑞 th ( 𝑞 ≥ 1 ) power are ( 𝛼 , 𝑚 )-convex. Some applications to special means of positive real numbers are also given.