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Sharp bounds for Seiffert means in terms of Lehmer means. (English) Zbl 1204.26053
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:
 2.6e+61 Means
##### Keywords:
Lehmer mean; first Seiffert mean; second Seiffert mean
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