二元广义平均的对数凸性及其应用
Bivariate log-convexity of the more extended means and its applications
摘要：
研究了参数对中双参数齐次函数的二元对数凸性。从这个二元对数凸性的更广泛的手段相对于一个参数对解决。Stolarsky平均、Gini平均、双参数identric（指数）平均和双参数Heronian平均关于参数在$\mathbb{[}0\mathbb{,\infty )}^{2}$上都是二元对数凹的，在$% \mathbb{(-\infty ,}0\mathbb{]}^{2}$上都是对数凸的.最后，给出了一些经典的和新的平均不等式。
英文摘要：
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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