Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 943534, 13 pages
doi:10.1155/2009/943534
Research Article

Abstract Convexity and Hermite-Hadamard Type Inequalities

Gabil R. Adilov1 and Serap Kemali2

1Department of Primary Education, Faculty of Education, Mersin University, 33169 Mersin, Turkey
2Vocational School of Technical Sciences, Akdeniz University, 07058 Antalya, Turkey

Received 24 February 2009; Accepted 8 May 2009

Academic Editor: Kunquan Lan

Copyright © 2009 Gabil R. Adilov and Serap Kemali. 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 deriving Hermite-Hadamard type inequalities for certain classes of abstract convex functions are considered totally, the inequalities derived for some of these classes before are summarized, new inequalities for others are obtained, and for one class of these functions the results on R+2 are generalized to Rn+. By considering a concrete area in R++n, the derived inequalities are illustrated.