Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 930294, 9 pages
Research Article

Sharpening and Generalizations of Shafer's Inequality for the Arc Tangent Function

1Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City 300160, China
2Department of Mathematics, Nanyang Normal University, Nanyang City, Henan Province 473061, China
3School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China

Received 18 March 2009; Revised 29 June 2009; Accepted 7 July 2009

Academic Editor: Martin J. Bohner

Copyright © 2009 Feng Qi 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 sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.