詹生（Jensen）不等式的推广

The Generalization of Jensen's Inequalities

本文所推导的定理均是将Ｊｅｎｓｅｎ不等式及其积分形式拓广为ｍ维，并将原定理中加权平均值或算术平均值概念推广成与（其中所有αｉ＞０，且）的形式得出。Ｊｅｎｓｅｎ不等式只是本文所述定理的一个特例（即令ｍ＝１．ｇ（ｘ）≡ｘ即得）。所以本文所述定理可使由詹生不等式导出的某些重要不等式得以进一步推广。

When generalized from one dimension to m dimensions,and with the redefined conception mean value as g-1,the Jensen's Incqualities and the integral form turn into the theorems of the thesis.Jensen's Incqualities can be considered as a special case of these theorems(Whcn m=1 and g(x)≡x,we will obtain Jensen's Inequalities respectively).Thus,somc of the important inequalities based on Jensen's Inequalities can be generalized too.