Asymptotic behavior of relatively nonexpansive operators in banach spaces

D. Butnariu, S. Reich, A. J. Zaslavski

Research output: Contribution to journalArticlepeer-review


Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

Original languageEnglish
Pages (from-to)151-174
Number of pages24
JournalJournal of Applied Analysis
Issue number2
StatePublished - Dec 2001

Bibliographical note

Funding Information:
The work of the first two authors was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grants 293/97 and 592/00). The second author was also partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — E. and M. Mendelson Research Fund.


  • Bregman distance
  • Convex function
  • Fixed point
  • Generic property
  • Iterative algorithm
  • Uniform space

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Asymptotic behavior of relatively nonexpansive operators in banach spaces'. Together they form a unique fingerprint.

Cite this