Certain sufficient conditions for starlikeness and convexity using a multiplier transformation

Richa Brar, Sukhwinder Singh Billing

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.

Keywords


analytic function, parabolic starlike function, uniformly convex function, starlike function, convex function, differential subordination, multiplier transformation.

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2018.3.06

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