PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Strony
1--11
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
autor
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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD4-0005-0048
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.