关于Cauchy不等式及其应用的探讨

The Application of Cauchy-inequality in Some Inner Product Spaces

文章主要给出了欧氏空间、n维实空间Rn、连续函数空间C[a,b]以及概率空间(Ω,F,P)中的Cauchy不等式,并探讨了其在求解和证明初等几何问题、最大值和最小值问题、函数极限问题、相关系数问题等方面的应用。

Cauchy--inequality is a very important inequality. This paper discusses the application of Cauchy--inequality in Euclidean space, n--dimensional real space, continuous function space, probability space. Some examples are provided in this paper about problems of maximum and minimum value, elementary geometry, and the limit of a function and coefficient of correlation.