Some extensions of the Open Door Lemma
Keywords:
Open door function, subordination.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 sucient condition for an analytic function on the unit disk to have positive real part. Kuroki and Owa modied the lemma when the initial point is non-real. In the present note, by extending their methods, we give a sucient condition for an analytic function on the unit disk to take its values in a given sector.
Mathematics Subject Classification (2010): 30C45, 30C80.
References
Duren, P.L., Univalent Functions, Springer-Verlag, 1983.
Kuroki, K., Owa, S., Notes on the open door lemma, Rend. Semin. Mat. Univ. Politec. Torino, 70(2012), 423434.
Miller, S.S., Mocanu, P.T., Briot-Bouquet di_erential equations and differential subordinations, Complex Variables Theory Appl., 33(1997), 217-237.
Miller, S.S., Mocanu, P.T., Differential subordinations. Theory and applications, Marcel Dekker, Inc., New York, 2000.
Mocanu, P.T., On strongly-starlike and strongly-convex functions, Studia Univ. Babes-Bolyai Math., 31(1986), 16{21.
Mocanu, P.T., Alpha-convex integral operator and strongly starlike functions, Studia Univ. Babes-Bolyai, Math., 34(1989), 18{24.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
