An extension of Tychonoff’s fixed point theorem to pseudonorm adjoint topological vector spaces
Jinlu Li
Abstract
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.
Topics & Concepts
Locally convex topological vector spaceMathematicsTopological vector spaceExtension (predicate logic)Topological tensor productFixed-point theoremTychonoff spaceTopological spaceVector spaceTopology (electrical circuits)Fréchet spacePure mathematicsKakutani fixed-point theoremBrouwer fixed-point theoremDiscrete mathematicsSchauder fixed point theoremCombinatoricsInterpolation spaceFunctional analysisComputer scienceGeneChemistryBiochemistryProgramming languageOptimization and Variational AnalysisFixed Point Theorems AnalysisAdvanced Control Systems Optimization