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Abstrakty
We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when com- putational errors are present. We also showthat most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.
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Tom
Strony
1--11
Opis fizyczny
Bibliogr. 13 poz.
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autor
autor
autor
- University of Haifa. Department of Mathematics, 31905 Haifa, Israel, dbutnaru@math.haifa.ac.il.
Bibliografia
- [1] Browder, F. E. , On the convergence of successive approximations for nonlinear functional equations, Indag. Math. (N.S.) 30 (1968), 27-35.
- [2] Butnariu, D., Reich, S., Zaslavski, A. J., Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal. 7 (2001), 151-174.
- [3] Butnariu, D., Reich, S., Zaslavski, A. J., Convergence of fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces, in "Fixed Point Theory and its Applications", Yokohama Publishers, Yokohama, 2006, 11-32.
- [4] De Blasi, F. S., Myjak, J., Sur la porosite de l'ensemble des contractions san s point fixe, C. R. Acad. Sci. Paris ser. I Math. 308 (1989), 51-54.
- [5] Jachymski, J., An extension of A. Ostrowski's theorem on the round-off stability of iterations, Aequationes Math. 53 (1997), 242-253.
- [6] Jachymski, J., Józwik, I., Nonlinear contractive conditions: a comparison and related problems, Banach Center Publ. 77 (2007), 123-146.
- [7] Krasnosel'skii, M. A., Zabreiko, P. P., Geometrical Methods of Nonlinear Analysis, Springer, Berlin, 1984.
- [8] Ostrowski, A. M., The round-off stability of iterations, ZAMM Z. Angew. Math. Mech. 47 (1967), 77-81.
- [9] Rakotch, E., A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459-465.
- [10] Reich, S., Shafrir, I., Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), 537-558.
- [11] Reich, S., Zaslavski, A. J., Convergence of generic infinite products of affine operators, Abstr. Appl. Anal. 4 (1999), 1-19.
- [12] Reich, S., Zaslavski, A. J., Convergence of generic infinite products of order-preserving mappings, Positivity 3 (1999), 1-21.
- [13] Reich, S., Zaslavski, A. J., The set of noncontractive mappings is σ-porous in the space of all non expansive mappings, C. R. Acad. Sci. Paris Ser. I Math. 333 (2001), 539-544.
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Bibliografia
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bwmeta1.element.baztech-article-LOD4-0005-0048