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- W2278244145 abstract "In the article, we prove that the double inequalities $M_{alpha }(a,b)< S_{QA}(a,b)< M_{beta}(a,b)$ and $M_{lambda }(a,b)< S_{AQ}(a,b)< M_{mu}(a,b)$ hold for all $a, b>0$ with $aneq b$ if and only if $alphaleqlog 2/[1+log2-sqrt{2}log(1+sqrt{2})]=1.5517ldots$ , $betageq5/3$ , $lambdaleq4log2/[4+2log2-pi]=1.2351ldots$ and $mugeq4/3$ , where $S_{QA}(a,b)=A(a,b)e^{Q(a,b)/M(a,b)-1}$ and $S_{AQ}(a,b)=Q(a,b)e^{A(a,b)/T(a,b)-1}$ are the Sandor-type means, $A(a,b)=(a+b)/2$ , $Q(a,b)=sqrt{(a^{2}+b^{2})/2}$ , $T(a,b)=(a-b)/[2arctan((a-b)/(a+b))]$ , and $M(a,b)=(a-b)/[2sinh ^{-1}((a-b)/(a+b))]$ are, respectively, the arithmetic, quadratic, second Seiffert, and Neuman-Sandor means." @default.
- W2278244145 created "2016-06-24" @default.
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- W2278244145 date "2016-02-16" @default.
- W2278244145 modified "2023-10-05" @default.
- W2278244145 title "Optimal bounds for two Sándor-type means in terms of power means" @default.
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- W2278244145 doi "https://doi.org/10.1186/s13660-016-0989-0" @default.
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