Contractive mappings and existence of cycle times for a monotone and homogeneous function |
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Authors: | Rolando Cavazos-Cadena,Daniel Herná ndez-Herná ndez |
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Affiliation: | 1. Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo COAH 25315, Mexico;2. Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato GTO 36000, Mexico |
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Abstract: | Given a monotone and homogeneous self-mapping f of the n-dimensional positive cone, a family of contractive mappings is used to define an equivalence relation in the index set, as well as a total order among the equivalence classes. Then, it is shown (i) that the cycle times are well-defined at each index belonging to the maximal and minimal classes, and (ii) that the cycle times of f exist at every index whenever a weak convexity condition is satisfied. |
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Keywords: | primary, 47J10 secondary, 47H09, 47H07 |
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