If =

S*[~] = { f E A: largzf'(z)//(z)l < ~ }, where ~ E (0, 1]. Since the next result holds for all ~ E (0, 2], we continue to use the notation S * [ ~ ] for ~ E ( 1 , 2], although a function in this class is not necessary starlike, nor even uninvalent. We first need to

prove the following lemma.