Sharp bounds for Seiffert means in terms of Lehmer means. (English) Zbl 1204.26053

Wang, Miao-Kun; Qiu, Ye-Fang; Chu, Yu-Ming

J. Math. Inequal. 4, No. 4, 581-586 (2010).

Summary: We establish two sharp inequalities as follows: \(P(a,b) > L_{-\frac 16} (a,b)\) and \(T (a,b) < L_{\frac 13} (a,b)\) for all \(a,b > 0\) with \(a = b\). Here, \(L_r(a,b), P(a,b)\) and \(T (a,b)\) are the 3 Lehmer, first and second Seiffert means of \(a\) and \(b\), respectively.

MSC:

26E60

Means

Keywords:

Lehmer mean; first Seiffert mean; second Seiffert mean