Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T00:41:37.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Pointwise Contraction Criteria for the Existence of Fixed Points

Published online by Cambridge University Press:  20 November 2018

Frank H. Clarke
Frank H. Clarke*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1W5
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.

We show that, in a complete metric space, every selfmap that is a “weak directional contraction” admits a fixed point.

Keywords

47H10contractionmetric convexityfixed point
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 7 - 11
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Clarke, F. H., Pointmse contraction criteria for the existence of fixed points, Technical Report 1658, Mathematics Research Center, University of Wisconsin, Madison.Google Scholar
2. Edelstein, M., An extension of Banach's contraction principles, Proc. Amer. Math. Soc. 12 (1961) 7-10.Google Scholar
3. Edelstein, M., On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962) 74-79.Google Scholar
4. Ekeland, I., On the variational principle, J. Math. Anal. Appl. 47 (1974) 324-353.Google Scholar
5. Kirk, W. A., Ray, W. O., A note on Lipschitzian mappings in convex metric spaces. To appear.Google Scholar
6. Smart, D. R., Fixed Point Theorems, Cambridge Tracts in Mathematics 66, Cambridge University Press, London (1974).Google Scholar