Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
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.
Czasopismo
Rocznik
Tom
Numer
Strony
123-154
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
- Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-950 Lublin, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-9