Sufficient Conditions for Subordination of Multivalent Functions
© Öznur Özkan Kılıç. 2008
Received: 13 January 2008
Accepted: 28 March 2008
Published: 21 April 2008
The authors investigate various subordination results for some subclasses of analytic functions in the unit disc. We obtain some sufficient conditions for multivalent close-to-starlikeness.
1. Introduction and Definitions
2. The Main Results
In proving our main results, we need the following lemma due to Miller and Mocanu.
Lemma 2.1 (see [3, page 132]).
and suppose that either
In addition, assume that
Thus, using Lemma 2.1 and (2.7), we can obtain the result (2.8).
Thus, using (2.15) and Lemma 2.4, we can obtain the result (2.16).
- Yang D: On a criterion for multivalently starlikeness. Taiwanese Journal of Mathematics 1997,1(2):143–148.MATHMathSciNetGoogle Scholar
- Özkan Ö, Altıntaş O: Applications of differential subordination. Applied Mathematics Letters 2006,19(8):728–734. 10.1016/j.aml.2005.09.002MATHMathSciNetView ArticleGoogle Scholar
- Miller SS, Mocanu PT: Differential Subordinations: Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 225. Marcel Dekker, New York, NY, USA; 2000:xii+459.Google Scholar
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