An Extension of Tychonoff Fixed Point Theorem

Jinlu Li

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arXiv · 1912.12768

An Extension of Tychonoff Fixed Point Theorem

Jinlu Li

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Abstract

In this paper, we introduce the concepts of weaknorm, quasi-weaknorm on real vector spaces. By these concepts, we introduce the concept of quasi-locally convex topological vector spaces, which include locally convex topological vector spaces as special cases. By the Fan-KKM theorem, we prove a fixed point theorem in quasi-locally convex topological vector spaces, that is a natural extension of Tychonoff fixed point theorem in locally convex topological vector spaces. Then we provide an example to show that this extension is a proper extension.

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Jinlu Li. 2019-12-30. An Extension of Tychonoff Fixed Point Theorem. https://arxiv.org/abs/1912.12768

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