Abstract
In this paper, we prove that the n-collinear elements x(1), x(2),...,x(n),u satisfy some special relations in an n-normed space X. Further, we prove that u = x(1)+...+x(n)/n is the only unique element in the n-normed space X such that x(1), x(2),...,x(n),u are n-collinear elements in X satisfying some specified inequalities. Moreover, we prove that the Riesz theorem holds when X is a linear n-normed space. (C) 2016 All rights reserved.