Fixed points for convex continuous mappings in topological vector spaces

Chen, Yu-Qing

doi:10.1090/S0002-9939-00-05767-1

Fixed points for convex continuous mappings in topological vector spaces
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by Yu-Qing Chen PDF

Proc. Amer. Math. Soc. 129 (2001), 2157-2162 Request permission

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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