2024/02/25 by Mai, Jiehua, Shi, Enhui, Yan, Kesong +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2402.16076
openalex publication_date 2024/02/25 · openalex created_date 2024/02/28 · openalex updated_date 2026/07/28
For a disk D in the plane \mathbb R2 and a plane map f, we give several conditions on the restriction of f to the boundary ∂ D of D which imply the existence of a fixed point of f in some specified domain in D. These conditions are similar to those appeared in the intermediate value theorem for maps on the real line. As an application of the main results, we establish a fixed point theorem for plane maps having an outflanking arc, which extends the famous theorem due to Brouwer: if f is an orientation-preserving homeomorphism on the plane and has a periodic point, then it has a fixed point.