Equivalence of communication and projective boundedness properties for monotone and homogeneous functions |
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Authors: | Rolando Cavazos-Cadena |
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Institution: | Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo, COAH 25315, Mexico |
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Abstract: | This work concerns the eigenvalue problem for a monotone and homogeneous self-mapping f of a finite-dimensional positive cone. A communication criterion is formulated such that it is equivalent to the projective boundedness of the upper eigenspaces associated with f, a property that yields the existence of a nonlinear eigenvalue. Using the idea of dual function, a similar result is obtained for lower eigenspaces. |
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Keywords: | primary 47J10 secondary 47H09 47H07 |
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