Taiwanese Journal of Mathematics

INEXACT ORBITS OF NONEXPANSIVE MAPPINGS

Evgeniy Pustylnik, Simeon Reich, and Alexander J. Zaslavski

Full-text: Open access

PDF File (158 KB)

Abstract

We study the influence of errors on the convergence of orbits of nonexpansive mappings in Banach and metric spaces.

Article information

Source
Taiwanese J. Math., Volume 12, Number 6 (2008), 1511-1523.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405037

Digital Object Identifier
doi:10.11650/twjm/1500405037

Mathematical Reviews number (MathSciNet)
MR2444869

Zentralblatt MATH identifier
1172.47052

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54E50: Complete metric spaces

Keywords
attractor Banach space complete metric space fixed point inexact orbit iteration nonexpansive mapping

Citation

Pustylnik, Evgeniy; Reich, Simeon; Zaslavski, Alexander J. INEXACT ORBITS OF NONEXPANSIVE MAPPINGS. Taiwanese J. Math. 12 (2008), no. 6, 1511--1523. doi:10.11650/twjm/1500405037. https://projecteuclid.org/euclid.twjm/1500405037


Export citation

References

  • [1.] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.
  • [2.] D. Butnariu, S. Reich and A. J. Zaslavski, Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces, Fixed Point Theory and its Applications, Yokahama Publishers, Yokahama, 2006, 11-32.
    Zentralblatt MATH: 1116.47052
  • [3.] D. Butnariu, S. Reich and A. J. Zaslavski, Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces, Journal of Applied Analysis, 13 (2007) 1-11.
    Mathematical Reviews (MathSciNet): MR2343874
    Zentralblatt MATH: 1138.54032
    Digital Object Identifier: doi:10.1515/JAA.2007.1
  • [4.] F. S. De Blasi and J. Myjak, Sur la convergence des approximations successives pour les contractions non linéaires dans un espace de Banach, C. R. Acad. Sci. Paris, 283 (1976), 185-187.
    Zentralblatt MATH: 0332.47028
  • [5.] F. S. De Blasi and J. Myjak, Sur la porosité de l'ensemble des contractions sans point fixe, C. R. Acad. Sci. Paris, 308 (1989), 51-54.
    Mathematical Reviews (MathSciNet): MR980084
  • [6.] A. M. Ostrowski, The round-off stability of iterations, Z. Angew. Math. Mech., 47 (1967), 77-81.
    Mathematical Reviews (MathSciNet): MR216731
    Zentralblatt MATH: 0149.36601
    Digital Object Identifier: doi:10.1002/zamm.19670470202
  • [7.] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc., 13 (1962), 459-465.
  • [8.] S. Reich and A. J. Zaslavski, Almost all nonexpansive mappings are contractive, C. R. Math. Rep. Acad. Sci. Canada, 22 (2000), 118-124.
    Zentralblatt MATH: 0971.47039
  • [9.] S. Reich and A. J. Zaslavski, The set of noncontractive mappings is $\sigma$-porous in the space of all nonexpansive mappings, C. R. Acad. Sci. Paris, 333 (2001), 539-544.
    Mathematical Reviews (MathSciNet): MR1860926
    Zentralblatt MATH: 1001.47036
    Digital Object Identifier: doi:10.1016/S0764-4442(01)02087-0
  • [10.] S. Reich and A. J. Zaslavski, Generic aspects of metric fixed point theory, Handbook of Metric Fixed Point Theory, Kluwer Dordrecht, 2001, pp. 557-575.
    Zentralblatt MATH: 1016.54021

Mathematical Society of the Republic of China

Taiwanese Journal of Mathematics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more