对称函数的一些不等式及其应用

SOME INEQUALITIES FOR SYMMETRIC FUNCTIONS AND APPLICATIONS

建立了下列对称函数的不等式：（ｉ）若ｘｉ＞０，ｉ＝１，…，ｎ，则当０＜ｔ＜１时，（ｉｉ）若ｘｉ＞０，ｉ＝１，…，ｎ，则当ｔ＞０时，ｔ＜０，ｘｉ＜１／｜ｔ｜，ｉ＝１，…，ｎ时，不等号反向．作为应用，文中还给出了四个三角函数的不等式．

The following inequalities for symmetric functions were established:The inequality ig readed for t<0 and 0<xi< 1/|t|, i= 1,..., n. Moreover, four inequalities of trigonometric functions were also established by the above inequalities and some given results.