Remarks on inequalities for the tangent function

Abstract

In the paper, the authors analyze and compare two double inequali- ties for bounding the tangent function, reorganize the proof in C.-P. Chen and F. Qi (A double inequality for remainder of power series of tangent function, Tamkang J. Math. 34 (4), 351–355, 2003) by using the usual definition of Bernoulli numbers, and correct some errors on page 6, (1.29) and (1.30) of F. Qi, D. -W. Niu, and B. -N. Guo (Re- finements, generalizations, and applications of Jordan’s inequality and related problems, J. Inequal. Appl. 2009 (2009), Article ID 271923, 52 pages, 2009). Moreover, the authors propose a sharp double inequality as a conjecture.