A Schur type inequality for five variables II

摘要

The purpose of this paper is to deduce a Schur type inequality for five variables. Let us consider three real variables x, y, t ∈ R such that x, y ≥ 0 and t > 0. Then x~t(x-y) + y~t(y-x) ≥ 0. Indeed, without loss of generality we can suppose, that x ≥ y ≥ 0. This means x~t ≥ y~t for t > 0. Consequently (x-y)(x~t-y~t) ≥ 0 i.e.