Landau problem for the class of functions that are regular in an annulus

Abstract

The classical result of Landau, establishing the radius of the largest circle, in which, for any function f(z)ɛR, where R is the class of regular functions w=f(z)=z+c2z2+..., in¦z¦<1, ¦f(z)¦<M for ¦z¦<1, the inverse function z=g(w), g(o)=o, exists and it is regular, is extended to the class of functions that are regular in a circular annulus.