Geodesic
Pointwise Contraction Criteria for the Existence of Fixed Points
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 7-11

Voir la notice de l'article provenant de la source Cambridge University Press

We show that, in a complete metric space, every selfmap that is a “weak directional contraction” admits a fixed point.
DOI : 10.4153/CMB-1978-002-8
Mots-clés : 47H10, contraction, metric convexity, fixed point 
Clarke, Frank H. Pointwise Contraction Criteria for the Existence of Fixed Points. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 7-11. doi: 10.4153/CMB-1978-002-8
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[1] 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] 2. Edelstein, M., An extension of Banach's contraction principles, Proc. Amer. Math. Soc. 12 (1961) 7-10. Google Scholar

[3] 3. Edelstein, M., On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962) 74-79. Google Scholar

[4] 4. Ekeland, I., On the variational principle, J. Math. Anal. Appl. 47 (1974) 324-353. Google Scholar

[5] 5. Kirk, W. A., Ray, W. O., A note on Lipschitzian mappings in convex metric spaces. To appear. Google Scholar

[6] 6. Smart, D. R., Fixed Point Theorems, Cambridge Tracts in Mathematics 66, Cambridge University Press, London (1974). Google Scholar

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