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arXiv · 1210.3875

Sharp Inequalities between Harmonic, Seiffert, Quadratic and Contraharmonic Means

Gen-Di Wang·Chen-Yan Yang·Yu-Ming Chu
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Abstract

In this paper, we present the greatest values $\alpha$, $\lambda$ and $p$, and the least values $\beta$, $\mu$ and $q$ such that the double inequalities $\alpha D(a,b)+(1-\alpha)H(a,b) 0$ with $a\neq b$, where $H(a,b)=2ab/(a+b)$, $T(a,b)=(a-b)/[2\arctan((a-b)/(a+b))]$, $Q(a,b)=\sqrt{(a^2+b^2)/2}$, $C(a,b)=(a^2+b^2)/(a+b)$ and $D(a,b)=(a^3+b^3)/(a^2+b^2)$ are the harmonic, Seiffert, quadratic, first contraharmonic and second contraharmonic means of $a$ and $b$, respectively.

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Gen-Di Wang, Chen-Yan Yang, Yu-Ming Chu. 2012-10-15. Sharp Inequalities between Harmonic, Seiffert, Quadratic and Contraharmonic Means. https://arxiv.org/abs/1210.3875

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