On generalizations of Schur's inequality

Abstract

Schur's inequality for the sum of products of the differences of real numbers states that for $x,y,z,t\ge 0$, $x^t(x-y)(x-z)+y^t(y-z)(y-x)+z^t(z-x)(z-y)\ge 0$. 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.

17 pages, 1 table

References in corpus (1)

• On rearrangement inequalities for multiple sequences

Cited by in corpus (1)

• On rearrangement inequalities for multiple sequences