2021/11/16 by Chen, Gangqiang
#30C80 #30F45 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.08555
Let z0 and w0 be given points in the open unit disk \mathbbD with |w0| < |z0|, and H0 be the class of all analytic self-maps f of \mathbbD normalized by f(0)=0. In this paper, we establish the fourth-order Dieudonné's Lemma and apply it to determine the variability region \f(4)(z0): f∈ H0,f(z0) =w0, f'(z0)=w1, f''(z0)=w2\ for given z0,w0,w1,w2 and give the form of all the extremal functions.