广义对数均值的单调性和凹凸性

Monotonicity and Convexity of the Generalized Logarithmic Mean

拓广平均由K.B.Stolarsky给出定义并列出其各种形式,而大部分含有两个变量的平均值都是拓广平均值的某种特殊情形.文章给出拓广平均值的一类情形,并利用有关中值定理和导数工具着重讨论了此类平均值函数的单调性、凹凸性.

The study is based on kiwifruit in Yuexi county, Anhui province. The relationship between the resistance of Ki-wifruit cuhivars to pseuomonas syringae pv. actinidae and the soluble protein content in branch （phloem） in the four seasons of the year 2005-2006 is studied. The result of linear regression shows that the soluble protein content correlates with the resistant type of the plant during October 2005 to January 2006. Their correlation coefficients are - 0.969 and -0. 887 respectively. The regression equation are Y = 8.712-50.718 X and Y = 34.590-226. 357X respectively.