On n-collinear elements and Riesz theorem

Abstract

In this paper, we prove that the n-collinear elements x1, x2,…, xn, u satisfy some special relations in an n-normed space X. Further, we prove that u = (Formula presented) is the only unique element in the n-normed space X such that x1, x2,…, xn; 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.