Two sharp double inequalities for Seiffert mean

Abstract

Abstract In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, 29, 221-222, 1995), and the methods from Chu et al. (J. Math. Inequal., 4, 581-586, 2010). The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. Mathematics Subject Classification (2010): 26E60.

Keywords

• Root-square mean
• arithmetic mean
• Seiffert mean