On generalizations of Schur's inequality
Abstract
Schur's inequality for the sum of products of the differences of real numbers states that for x,y,z,t≥ 0, xt(x-y)(x-z) + yt(y-z)(y-x) + zt(z-x)(z-y) ≥ 0. In this paper we study a generalization of this inequality to more terms, more general functions of the variables and algebraic structures such as vectors and Hermitian matrices.
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