Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/32882
Title: Positive eigenvalue-eigenvector of nonlinear positive mappings
Authors: Song, Y
Qi, L 
Keywords: Edelstein contraction
Eigenvalue-eigenvector
Homogeneous mapping
Nonnegative tensor
Strongly increasing
Issue Date: 2014
Publisher: Higher Education Press
Source: Frontiers of mathematics in China, 2014, v. 9, no. 1, p. 181-199 How to cite?
Journal: Frontiers of mathematics in China 
Abstract: We show that an (eventually) strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert's projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein-Rutman theorem is presented, and a simple iteration process {Tk x/{norm of matrix}Tk x{norm of matrix}} (∀ x ∈ P+) is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert's projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.
URI: http://hdl.handle.net/10397/32882
ISSN: 1673-3452
EISSN: 1673-3576
DOI: 10.1007/s11464-013-0258-1
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