Journal of Applied Mathematics
Volume 2011 (2011), Article ID 869261, 9 pages
Research Article

Some Refinements of Inequalities for Circular Functions

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

Received 22 August 2011; Accepted 4 October 2011

Academic Editor: Morteza Rafei

Copyright © 2011 Zhengjie Sun and Ling 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.


We give new lower bound and upper bound for Papenfuss-Bach inequality and improve Ruehr-Shafer inequality by providing a new lower bound.