Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T06:19:50.915Z Has data issue: false hasContentIssue false
  • English
  • Français

On successive approximations for nonexpansive mappings in Banach spaces†

Published online by Cambridge University Press:  18 May 2009

W. A. Kirk
W. A. Kirk
Affiliation:
University of Iowa, Iowa City, Iowa 52240, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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.

Let X be a Banach space and K a convex subset of X. A mapping Tof K into K is called a nonexpansive mapping if | T(x) – T(y) | ≦ | x – y | for all x, yεK.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 1 , April 1971 , pp. 6 - 9
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

1.Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 1041–1044.CrossRefGoogle Scholar
l2.Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660–665.CrossRefGoogle Scholar
3.Browder, F. E. and Petryshyn, W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571–575.CrossRefGoogle Scholar
4.Edelstein, M., A remark on a theorem of M. A. Krasnoselskii, Amer. Math. Monthly 73 (1966), 509–510.CrossRefGoogle Scholar
5.Gohde, D., Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251–258.CrossRefGoogle Scholar
6.Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
7.Krasnoselskii, M. A., Two remarks about the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123–127.Google Scholar
8.Schaefer, H., Ober die Methode suksessiver Approximation, Jber. Deutsch. Math. Verein. 59 (1957), 131–140.Google Scholar