2020/12/04 by Jinlu Li, Li, Jinlu
Computer Science · Mathematics · #06F30 #45G10 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2012.02345
openalex publication_date 2020/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the topological dual spaces) to quasi-point separable topological vector spaces by families of generalized m-quasiconvex functionals. We show that every pseudonorm adjoint topological vector space, which includes locally convex topological vector spaces as special cases, is quasi-point separable. By the Fan-KKM theorem, we prove a fixed point theorem on quasi-point separable topological vector spaces. It is an extension of the fixed point theorem on pseudonorm adjoint topological vector spaces proved in [8]. Therefore, it is a properextension of Tychonoffs fixed point theorem on locally convex topological vector spaces, which are demonstrated by some examples.