SCHUR–CONVEXITY OF THE COMPLETE SYMMETRIC FUNCTION

摘要

This paper investigates Schur-convexity of the complete symmetric function c_r(x) = ∑_(I_1 + ...+i_n = r~(x_1~ij...x_n~in) and the function φr(x) = (c_r(x))/(c_(r-1)(x)), where i_1, ..., i_n are non-negative integers and r ≥ 1. Some inequalities, including Ky Fan type inequality, are established by use of the theory of majorization. It is also concerned with an open problem proposed by Menon [1].