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    STUDIA MATHEMATICA - Issue no. 3 / 2015  
         
  Article:   SOME EXTENSIONS OF THE OPEN DOOR LEMMA.

Authors:  . 		 
       
         
  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.

Mathematics Subject Classification (2010): 30C45, 30C80.

Keywords: Open door function, subordination. 		 
         
     
         
         
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