Some extensions of the Open Door Lemma
Complex Variables
2015-02-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1502.05123,
title = {Some extensions of the Open Door Lemma},
author = {Ming Li and Toshiyuki Sugawa},
journal= {arXiv preprint arXiv:1502.05123},
year = {2015}
}
Comments
10 pages, 1 figure