On sufficient conditions for analytic functions to be Bazilevi[cbreve]

Abstract

The purpose of the present article is to establish two theorems for a class of analytic univalent functions defined in the open unit disk. The results are proved by using techniques involving the principle of differential subordination. Connections of these theorems with Bazilevic˘ functions are considered and the main results are applied to obtain sufficient conditions for analytic functions to be starlike and close-to-convex.

Keywords:

• subordination
• analytic univalent functions
• Bazilevic˘ functions
• starlike functions
• close-to-convex functions

AMS Subject Classification::

• 30C45

Acknowledgements

The authors are grateful to worthy referees for their valuable suggestions. P. Goswami is also thankful to CSIR, India, for providing JRF under research scheme no. 09/135(0434)/2006-EMR-1.