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Sharp power-type Heronian mean bounds for the Sándor and Yang means. (English) Zbl 1372.26032
Summary: We prove that the double inequalities $$H_{\alpha}(a, b) < X(a, b)<H_{\beta}(a, b)$$ and $$H_{\lambda}(a, b)< U(a, b)<H_{\mu}(a, b)$$ hold for all $$a, b>0$$ with $$a\neq b$$ if and only if $$\alpha\leq 1/2$$, $$\beta\geq\log 3/(1+\log2)=0.6488\dots$$, $$\lambda\leq 2\log 3/(2\log\pi-\log 2) =1.3764\dots$$, and $$\mu\geq 2$$, where $$H_{p}(a, b)$$, $$X(a, b)$$, and $$U(a, b)$$ are, respectively, the $$p$$th power-type Heronian mean, Sándor mean, and Yang mean of $$a$$ and $$b$$.

##### MSC:
 2.6e+61 Means
##### Keywords:
power-type Heronian mean; Sándor mean; Yang mean
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##### References:
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