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Abstract and Applied Analysis
Volume 2014, Article ID 636751, 7 pages
http://dx.doi.org/10.1155/2014/636751
Research Article

Generalized Convex Functions on Fractal Sets and Two Related Inequalities

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 25 March 2014; Revised 20 May 2014; Accepted 30 May 2014; Published 15 June 2014

Academic Editor: Praveen Agarwal

Copyright © 2014 Huixia Mo et al. 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

We introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen’s inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.