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arXiv · 1408.2252

Bivariate log-convexity of the more extended means and its applications

Zhen-Hang Yang
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Abstract

In this paper, the bivariate log-convexity of the two-parameter homogeneous function in parameter pair is vestigated. From this the bivariate log-convexity of the more extended means with respect to a parameter pair is solved. It follows that Stolarsky means, Gini means, two-parameter identric (exponential) means and two-parameter Heronian means are all bivariate log-concave on $\mathbb{[}0\mathbb{,\infty )}^{2}$ and log-convex on $% \mathbb{(-\infty ,}0\mathbb{]}^{2}$ with respect to parameters. Lastly, some classical and new inequalities for means are given.

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Zhen-Hang Yang. 2014-08-10. Bivariate log-convexity of the more extended means and its applications. https://arxiv.org/abs/1408.2252

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