Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T02:41:11.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Finding common fixed points of nonexpansive mappings by iteration

Published online by Cambridge University Press:  17 April 2009

B. E. Rhoades
B. E. Rhoades
Affiliation:
Department of Mathematics, Indiana University, Bloomington IN 47405–7106, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper it is shown that a particular iteration scheme converges weakly to a common fixed point of a finite set of nonexpansive mappings. This result is an improvement of two related theorems in the literature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 307 - 310
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Atsushiba, S. and Takahashi, W., ‘Approximating common fixed points of two nonexpansive mappings in Banach spaces’, Bull. Austral. Math. Soc. 57 (1999), 117–127.CrossRefGoogle Scholar
[2]Browder, F.E., ‘Some contractive and semiaccretive nonlinear mappings in Banach spaces’, Bull. Amer. Math. Soc. 74 (1968), 660–665.CrossRefGoogle Scholar
[3]Ishikawa, S., ‘Fixed points and iteration of a nonexpansive mapping in a Banach space’, Proc. Amer. Math. Soc. 59 (1976), 65–71.CrossRefGoogle Scholar
[4]Kuhfittig, P.K.F., ‘Common fixed points of nonexpansive mappings by iteration’, Pacific J. Math. 97 (1981), 137–139.CrossRefGoogle Scholar