%0 Journal Article
%T Some extensions of the Open Door Lemma
%A Ming Li
%A Toshiyuki Sugawa
%J Mathematics
%D 2015
%I arXiv
%X Miller and Mocanu proved in their 1997 paper a greatly useful result which is now known as the Open Door Lemma. It provides a sufficient condition for an analytic function on the unit disk to have positive real part. Kuroki and Owa modified the lemma when the initial point is non-real. In the present note, by extending their methods, we give a sufficient condition for an analytic function on the unit disk to take its values in a given sector.
%U http://arxiv.org/abs/1502.05123v1