ky fan theorem
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2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Mohsen Tourang ◽  
Mostafa Zangiabadi

AbstractThe improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315–335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817–1834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.


2014 ◽  
Vol 459 ◽  
pp. 23-42 ◽  
Author(s):  
Ivan Gutman ◽  
Enide A. Martins ◽  
María Robbiano ◽  
Bernardo San Martín
Keyword(s):  
Ky Fan ◽  

2005 ◽  
Vol 49 (5-6) ◽  
pp. 789-803 ◽  
Author(s):  
Hou-Biao Li ◽  
Ting-Zhu Huang

2003 ◽  
Vol 369 ◽  
pp. 77-93 ◽  
Author(s):  
Ivica Nakić ◽  
Krešimir Veselić
Keyword(s):  
Ky Fan ◽  

1959 ◽  
Vol 11 (4) ◽  
pp. 231-235 ◽  
Author(s):  
L. Mirsky

Making use of properties of doubly-stochastic matrices, I recently gave a simple proof (4) of a theorem of Ky Fan (Theorem 2b below) on symmetric gauge functions. I now propose to show that the same idea can be employed to derive a whole series of results on convex functions ; in particular, certain well-known inequalities of Hardy-Littlewood-Pólya and of Pólya will emerge as specìal cases.


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