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Sharp power mean bounds for the combination of Seiffert and geometric means. (English) Zbl 1197.26054
Summary: We answer the question: for $$\alpha \in (0,1)$$, what are the greatest value $$p$$ and the least value $$q$$ such that the double inequality $$M_{p}(a,b)<P^\alpha(a,b)G^{1-\alpha}(a,b)<M_q(a,b)$$ holds for all $$a,b>0$$ with $$a\neq b$$. Here, $$M_{p}(a,b)$$, $$P(a,b)$$, and $$G(a,b)$$ denote the power of order $$p$$, Seiffert, and geometric means of two positive numbers $$a$$ and $$b$$, respectively.

##### MSC:
 2.6e+61 Means
Full Text:
##### References:
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