Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 130821, 10 pages
Research Article

Inequalities for Hyperbolic Functions and Their Applications

Department of Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310018, China

Received 9 April 2010; Accepted 15 May 2010

Academic Editor: Wing-Sum Cheung

Copyright © 2010 L. Zhu. 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.


A basic theorem is established and found to be a source of inequalities for hyperbolic functions, such as the ones of Cusa, Huygens, Wilker, Sandor-Bencze, Carlson, Shafer-Fink type inequality, and the one in the form of Oppenheim's problem. Furthermore, these inequalities described above will be extended by this basic theorem.