Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 840206, 10 pages
Research Article

On Shafer and Carlson Inequalities

1School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454003, China
2Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
3Department of Mathematics, Hechi University, Yizhou, Guangxi 546300, China

Received 23 November 2010; Accepted 5 February 2011

Academic Editor: Martin Bohner

Copyright © 2011 Chao-Ping Chen 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.


We present a generalized and sharp version of Shafer's inequality for the inverse tangent function and a new lower bound of Carlson's inequality by means of a third order estimate of the inverse cosine function.