Lower and upper bounds for ω-limit sets of nonexpansive maps

Indagationes Mathematicae

Volumn 12, Issue 2, 2001, Pages 191-211

  Lemmens, B ^a   Nussbaum, R D ^b   Verduyn Lunel, S M ^c  

^a Vrge Vniversiteit Amsterdam   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035908296     PISSN: 00193577     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0019-3577(01)80025-2     Document Type: Article

References (18)

1. Akcoglu M.A., Krengel U. Nonlinear models of diffusion on a finite space. Probab. Theory Related Fields. 76:1987;411-420.
2. Alon N., Füredi Z., Katchalski M. Separating pairs of points by standard boxes. European J. Combin. 6:1985;205-210.
3. Dafermos C.M., Slemrod M. Asymptotic behaviour of nonlinear contraction semi-groups. J. Funct. Anal. 13:1973;97-106.
4. Erdód́s P., Szekeres G. A combinatorial problem in geometry. Compositio Math. 2:1935;463-470.
5. Kruskal J.B. Monotonic subsequences. Proc. Amer. Math. Soc. 4:1953;264-274.
6. Lemmens B. Integral rigid sets and periods of nonexpansive maps. Indag. Mathem. N.S. 10:1999;437-447.
7. Lyons R., Nussbaum R.D. On transitive and commutative finite groups of isometries. Tan K.-K., Fixed Point Theory and Applications. 1992;189-228 World Scientific, Singapore.
8. Martus P. Asymptotic properties of nonstationary operator sequences in the nonlinear case. Ph.D. dissertation. 1989;Friedrich-Alexander Univ. Erlangen-Nürnberg. (in German).
9. 1-spaces. Report, Mathematica Göttingensis Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis. 1987;. Heft 45.
10. Nussbaum R.D. Omega limit sets of nonexpansive maps: finiteness and cardinality estimates. Differential Integral Equations. 3:1990;523-540.
11. Nussbaum R.D. Estimates of the periods of periodic points of nonexpansive operators. Israel J. Math. 76:1991;345-380.
12. Nussbaum R.D. A nonlinear generalization of Perron-Frobenius theory and periodic points of nonexpansive maps. Censor Y., Reich S., Recent Developments in Optimization Theory and Nonlinear Analysis. 204:1997;183-198 American Math. Society, Providence, R.I. Contemporary Mathematics.
13. Nussbaum R.D., Scheutzow M. Admissible arrays and a nonlinear generalization of Perron-Frobenius theory. J. London Math. Soc. 2:1998;526-544.
14. Nussbaum R.D., Scheutzow M., Verduyn Lunel S.M. Periodic points of nonexpansive maps and nonlinear generalizations of the Perron-Frobenius theory. Selecta Math. (N.S.). 4:1998;1-41.
15. Nussbaum R.D., Verduyn Lunel S.M. Generalizations of the Perron-Frobenius theorem for nonlinear maps. Memoirs of the American Mathematical Society. 138:(659):1999;1-98.
16. 1-spaces. European J. Combin. 9:1988;73-78.
17. 1-spaces. European J. Combin. 12:1991;183.
18. Weller D. Hilbert's metric, part metric and self mappings of a cone. Ph.D. dissertation. 1987;Univ. of Bremen, Germany.