Related papers: Extensions of the Schur majorisation inequalities

We study a variant of the majorization relation. In particular we consider inequalities involving some Schur-concave symmetric polynomials related to the multinomial expansion. We also discuss how these topics were motivated by conjectures…

For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.

We prove some extensions of Andrews inequality.

Schur's inequality states that the sum of three special terms is always nonnegative. This note is a short review of inequalities for the sum of the reciprocals of these terms and of extensions of the latter inequalities to an arbitrary…

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.

We obtain some new inequalities of Chebyshev Type.

We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of Strengthened Cauchy-Schwarz inequalities is derived using these identities. Also, an…

Certain new inequalities for the sums of factorials are presented.

Some inequalities for different types of convexity are established.

We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.

We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.

We study modular analogues of Schur numbers for systems of linear equations. We show that these only depend on the number of equations, not their coefficients and in the case of one equation show stronger bounds.

Schur's inequality for the sum of products of the differences of real numbers states that for $x,y,z,t\geq 0$, $x^t(x-y)(x-z) + y^t(y-z)(y-x) + z^t(z-x)(z-y) \geq 0$. In this paper we study a generalization of this inequality to more terms,…

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…

In this article we derive some polynomial inequalities for Mertens functions.

Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using…

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, we improve a bound due to I. Schur.