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Nonexpansive Mappings in Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

Troy L. Hicks  and
John D. Kubicek
Troy L. Hicks
Affiliation:
Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri65401
John D. Kubicek
Affiliation:
Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri65401
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Recently Bruck initiated the study of the structure of the fixed-point set of a nonexpansive selfmap T of a Banach space, where T satisfies a conditional fixed point property. We generalize many of his results to a Hausdorff locally convex space X. Also, we generalize a result of Holmes and Narayanaswami and use it, along with a procedure of Kiang, to obtain a fixed point theorem for families of asymptotically nonexpansive mappings in X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 455 - 461
Copyright
Copyright © Canadian Mathematical Society 1977

References

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