An extension of Tychonoff’s fixed point theorem to pseudonorm adjoint topological vector spaces
Jinlu Li · Optimization · 2020
In this paper, we introduce a type of pseudonorms and quasi-pseudonorms on real vector spaces. By these concepts, we introduce the concept of pseudonorm adjoint 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 pseudonorm adjoint topological vector spaces, that is a proper extension of Tychonoff’s fixed point theorem on locally convex topological vector spaces. Then we provide an example to show that this extension is indeed a proper extension.