Geodesic
On Fixed Point Theorems for Mappings in a Separated Locally Convex Space
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 603-604

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

The Banach contraction principle has been generalized by Tan [6] to the mappings in separated locally convex spaces. We show that the result of Sehgal [5] and also of Holmes [3] can be generalized in the same way.Throughout this note, we let X be a separated locally convex space, U a base for the closed absolutely convex neighborhoods of the origin O in X, K a nonempty subset of X, and Ta mapping from K to K. 
Lee, Cheng-Ming. On Fixed Point Theorems for Mappings in a Separated Locally Convex Space. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 603-604. doi: 10.4153/CMB-1972-106-8
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[1] 1. Bailey, D. F., Some theorems on contractive mappings, J. London Math. Soc. 41 (1966), 101-106. Google Scholar

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[5] 5. Sehgal, V. M., A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc. 23 (1969), 631-634. Google Scholar

[6] 6. Tan, K-K., Some fixed point theorems for non-expansive mappings in Hausdorff locally convex spaces, Ph.D. thesis, Univ. of British Columbia, Vancouver, B.C., Canada, 1970. Google Scholar

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