SCHUR CONVEXITY AND SCHUR MULTIPLICATIVE CONVEXITYFOR A CLASS OF SYMMETRIC FUNCTIONS WITH APPLICATIONS

摘要

For x = (x_1 ,x_2,..., x_n)E (0, 1 ]~nand re { I, 2, ... ,n },a symmetric functionF(x, r)isdefined by the relation where ii, i2, , in are positive integers. This paper deals with the Schur convexity and Schurmultiplicative convexity of F (x, r) . As applications, some inequalities are established by us-ing the theory of majorization.