2020/04/06 by Gangqiang Chen, Chen, Gangqiang, Hiroshi Yanagihara +1
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2004.02405
Let z0 and w0 be given points in the open unit disk \mathbbD with |w0| < |z0|. Let H0 be the class of all analytic self-maps f of \mathbbD normalized by f(0)=0, and H0 (z0,w0) = \ f ∈ H0 : f(z0) =w0\. In this paper, we explicitly determine the variability region of f''(z0) when f ranges over H0 (z0,w0). We also show a geometric view of our main result by Mathematica.