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Abstract and Applied Analysis
Volume 2014, Article ID 690803, 6 pages
Research Article

Inequalities for Convex Functions on Simplexes and Their Cones

1Mechanical Engineering Faculty in Slavonski Brod, University of Osijek, Trg Ivane Brlić Mažuranić 2, 35000 Slavonski Brod, Croatia
2Department of Mathematics and Computer Science, Longyan University, Longyan, Fujian 364012, China

Received 9 April 2014; Accepted 17 July 2014; Published 27 October 2014

Academic Editor: Vladimir Georgiev

Copyright © 2014 Zlatko Pavić and Shanhe Wu. 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.


The aim of this paper is to present the fundamental inequalities for convex functions on Euclidean spaces. The work is based on the geometry of the simplest convex sets and properties of convex functions. Some obtained inequalities are applied to demonstrate a natural way of generalizing the Hermite-Hadamard inequality.