Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/17379
Title: The existence and uniqueness of eigenvalues for monotone homogeneous mapping pairs
Authors: Song, Y
Qi, L 
Keywords: Collatz-Wielandt property
G-eigenvalue
G-eigenvector
Monotone homogeneous mapping pairs
Issue Date: 2012
Source: Nonlinear analysis, theory, methods and applications, 2012, v. 75, no. 13, p. 5283-5293 How to cite?
Journal: Nonlinear Analysis, Theory, Methods and Applications 
Abstract: In this paper, the concept of eigenvalue is introduced to the monotone homogeneous mapping pairs (f,g), and its existence and uniqueness are established successfully under the boundedness of some orbits of f,g in the Hilbert semi-norm. Also, the Collatz-Wielandt min-max type property is obtained for such a class of mapping pairs. In particular, the nonlinear Perron-Frobenius property for nonnegative tensor pairs (A,B) is obtained without involving the calculation of the tensor inversion. By particularizing the mapping g or f, several results can emerge as corollaries. They lead to further existence results and open problems.
URI: http://hdl.handle.net/10397/17379
ISSN: 0362-546X
DOI: 10.1016/j.na.2012.04.045
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