Criteria for the extremality of the Koebe mapping

Abstract

A criterion is developed which gives a necessary condition on a real functional in order that the Koebe Mapping be extremal for this functional in the well known class S S of normalized univalent functions. This is applied to the coefficient problem of [ f ( z ) ] λ , 0 > λ > 1 {[f(z)]^\lambda },0 > \lambda > 1 as well as to the problem of univalence of sections of the power series expansion of f ( z ) f(z) .