Certain sufficient conditions for starlikeness and convexity using a multiplier transformation
DOI:
https://doi.org/10.24193/subbmath.2018.3.06Keywords:
Analytic function, parabolic starlike function, uniformly convex function, starlike function, convex function, differential subordination, multiplier transformation.Abstract
In the present paper, we study a differential subordination involving a multiplier transformation. Selecting different dominants to our main result, we obtain certain sufficient conditions for starlikeness and convexity of analytic functions. In particular, we obtain the sufficient conditions for parabolic starlikeness and uniform convexity. Some known results appear as particular cases of our main result.
Mathematics Subject Classification (2010): 30C80, 30C45.
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