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Proceedings of the American Mathematical Society

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Fixed points for convex continuous mappings in topological vector spaces


Author: Yu-Qing Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 2157-2162
MSC (2000): Primary 54H25; Secondary 47H10
Published electronically: November 21, 2000
MathSciNet review: 1825929
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Abstract:

We prove the following result. Let $C$ be a convex compact subset in a topological vector space, and $T:C\to C$ a convex continuous mapping. (See Definition 1.1.) Then $T$ has a fixed point. Moreover, continuous mappings that can be approximated by convex continuous mappings also have the fixed point property.


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Additional Information

Yu-Qing Chen
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701-2979; Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China
Email: yuqchen@bing.math.ohiou.edu, nic2601@scu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05767-1
Keywords: Topological vector space, convex compact set, fixed point
Received by editor(s): July 14, 1999
Received by editor(s) in revised form: October 27, 1999
Published electronically: November 21, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society