The Landau problem for nonvanishing functions with real coefficients

摘要

For the class of holomorphic functions f(z)=f0+f1z+f2z2+⋯ in the unit disk |z|<1 with 0<|f(z)|<1 and fn∈R, n=0,1,2,… we prove that max(f0+f1+⋯+f4)=max|f0+f1+⋯+f4|=1.46109… and min(f0+f1+⋯+f4)=−0.713082….