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An extension of Schur-Ostrowski's condition, weak Eaton triples and generalized AI functions.
- Source :
-
Linear Algebra & its Applications . Nov2019, Vol. 580, p212-235. 24p. - Publication Year :
- 2019
-
Abstract
- In this paper, for a given Eaton triple (V , G , D) , we present a characterization of G -increasing real functions by using the maximality property of their directional derivatives. It generalizes Schur-Ostrowski's condition related to Schur-convexity of a function. It is also useful in establishing theorems of von Neumann-Davis type regarding the form of group-invariant real functions with certain kinds of convexity. We introduce and investigate weak Eaton triples and their chains. We show a method for constructing new Eaton triples. We apply it to define generalized arrangement-increasing (AI) functions. We prove that the mentioned derivatives of G -increasing maps are generalized AI functions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 580
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 138031357
- Full Text :
- https://doi.org/10.1016/j.laa.2019.06.025