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Optimal power mean bounds for Yang mean. (English) Zbl 1339.26086
Summary: In this paper, we prove that the double inequality $$M_p(a,b)<U(a,b)<M_q(a,b)$$ holds for all $$a,b>0$$ with $$a\neq b$$ if and only if $$p\leq 2\log 2/(2\log\pi-\log 2)=0.8684\ldots$$ and $$q\geq 4/3$$, where $$U(a,b)$$ and $$M_r(a,b)$$ are the Yang and $$r$$th power means of $$a$$ and $$b$$, respectively.

##### MSC:
 2.6e+61 Means
##### Keywords:
Yang mean; power mean; Neuman-Sándor mean
Full Text:
##### References:
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