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Jinlu Li, The fixed point property of quasi-point-separable topological vector spaces

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DOI: 10.23952/jano.5.2023.1.08
Volume 5, Issue 1, 1 April 2023, Pages 125-132

 

Abstract. In this paper, we introduce a new concept of quasi-point-separable topological vector spaces, which has the following important properties: (1) in general, the conditions for a topological vector space to be quasi-point-separable is not difficult to verify; (2) the class of quasi-point-separable topological vector spaces is large and includes locally convex topological vector spaces and pseudonorm adjoint topological vector spaces as special cases; (3) every quasi-point-separable Housdorrf topological vector space has the fixed point property (that is, every continuous self-mapping on any given nonempty closed and convex subset has a fixed point), which is the result of the main theorem of this paper. Finally, we provide some concrete examples of quasi-point-separable topological vector spaces, which are not locally convex.

 

How to Cite this Article:
J. Li, The fixed point property of quasi-point-separable topological vector spaces, J. Appl. Numer. Optim. 5 (2023), 125-132.