Majorization and relative concavity

Niezgoda, Marek

doi:10.1016/j.laa.2010.11.044

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…Theorem 7.5 ([58,Theorem 11]). Let (V, G, D) be an Eaton triple with M G (V ) = span v for some nonzero v ∈ V , v > 1.…”

Section: A Review Of Selected Topics In Majorization Theorymentioning

confidence: 99%

“…We focus on group majorizations, group-induced cone orderings, normal decomposition systems (ND systems), Eaton triples (E-systems) and similarly separable vectors. We quote the relevant material mainly from [48,50,51,54,55,57,56,58,59,60].…”

mentioning

confidence: 99%

“…Further applications are given in Section 7. Here Shi type inequalities are investigated [58]. As corollaries, some G-majorization extensions of Ky Fan inequality are presented.…”

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confidence: 99%

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A review of selected topics in majorization theory

Niezgoda¹

2013

Banach Center Publ.

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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.

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“…Theorem 7.5 ([58,Theorem 11]). Let (V, G, D) be an Eaton triple with M G (V ) = span v for some nonzero v ∈ V , v > 1.…”

Section: A Review Of Selected Topics In Majorization Theorymentioning

confidence: 99%