C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (4), 2005 pp. 121–128
September 30, 2005
Simeon Reich, Department of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel; email: sreich@tx.technion.ac.il
Alexander J. Zaslavski, Department of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel; email: ajzasl@tx.technion.ac.il
Abstract/Résumé:
Let \(K\) be a bounded, closed and convex subset of a Banach space \(X\). We show that the iterates of a typical element (in the sense of Baire category) of a class of nonexpansive mappings which take \(K\) to \(X\) converge uniformly on \(K\) to the unique fixed point of this typical element.
Soit \(K\) un sous-ensemble borné, fermé et convexe d’un espace de Banach \(X\). Nous démontrons que les itérés d’un élément typique (au sens des catégories de Baire) d’une classe d’applications non-expansives de \(K\) dans \(X\) convergent uniformément sur \(K\) vers l’unique point fixe de cet élément typique.
AMS Subject Classification: Nonexpansive mappings; and their generalizations (ultimately compact mappings; measures of noncompactness and condensing mappings; $A$-proper mappings; $K$-set contractions; etc.) 47H09
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