Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 919-940

THE DENJOY-WOLFF THEOREM FOR CONDENSING MAPPINGS IN A BOUNDED AND STRICTLY CONVEX DOMAIN IN A COMPLEX BANACH SPACE

Monika Budzynska

Uniwersytet Marii Curie-Sklodowskiej, Instytut Matematyki
20-031 Lublin, Poland; monikab1 'at' hektor.umcs.lublin.pl

Abstract. If D is a bounded and strictly convex domain in a complex Banach space and f : D → D is holomorphic, condensing with respect to the Kuratowski measure of noncompactness and fixed-point-free, then there exists ξ ∈ ∂D such that the sequence {fⁿ} of the iterates of f converges in the compact-open topology to the constant mapping taking the value ξ.

2010 Mathematics Subject Classification: Primary 32A10, 32A17, 46G20, 47H10.

Key words: Horosphere, iterates of holomorphic mappings, the Denjoy-Wolff theorem, the Kobayashi distance.

Reference to this article: M. Budzynska: The Denjoy-Wolff Theorem for condensing mappings in a bounded and strictly convex domain in a complex Banach space. Ann. Acad. Sci. Fenn. Math. 39 (2014), 919-940.

Full document as PDF file

doi:10.5186/aasfm.2014.3944