Two optimal double inequalities between power mean and logarithmic mean
نویسندگان
چکیده
منابع مشابه
Optimal Inequalities between Seiffert’s Mean and Power Means
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* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, ...
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For all $a,b>0$, the following two optimal inequalities are presented: $H^{alpha}(a,b)L^{1-alpha}(a,b)geq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ H^{alpha}(a,b)L^{1-alpha}(a,b)leq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. Here, $H(a,b)$, $L(a,b)$, and $M_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2010
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.04.032