A review of selected topics in majorization theory

• Autorzy: Marek Niezgoda
• Języki publikacji: EN

Abstrakty

EN

In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors are described. Generalizations of Hardy-Littlewood-Pólya Theorem and Schur-Ostrowski Theorem are presented. Generalized Schur-convex functions are investigated. Extensions of Ky Fan inequalities are provided. Applications to Grüss and Ostrowski type inequalities are given.

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
• 26D15: Inequalities for sums, series and integrals
• 15A42: Inequalities involving eigenvalues and eigenvectors
• 15A30: Algebraic systems of matrices
• 26A51: Convexity, generalizations
• 26D10: Inequalities involving derivatives and differential and integral operators
• 39B62: Functional inequalities, including subadditivity, convexity, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2013
• Tom: 99
• Numer: 1
• Strony: 123-154

Daty

wydano

2013

Twórcy

autor

Marek Niezgoda

• Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-950 Lublin, Poland

Identyfikatory

DOI

10.4064/bc99-0-9