On Certain Results Involving a Multiplier Transformation in a Parabolic Region

Document Type : Original Article

Authors

Richa Brar

Sukhwinder Singh Billing

Department of Mathematics, Sri Guru Granth Sahib World University , Fatehgarh Sahib-140407, Punjab, India.

10.22034/kjm.2018.59751

Abstract

We, here, obtain certain results in subordination form involving a multiplier transformation in a parabolic region. In particular, using different dominants in our main result, we derive certain results on parabolic starlikeness, starlikeness, convexity, uniform convexity, strongly starlikeness, close-to-convexity and uniform close-to-convexity of p-valent analytic functions as well as univalent analytic functions.

Keywords

Analytic function

parabolic starlike function

uniformly convex function

differential subordination

multiplier transformation

Subjects

• 30 Functions of a complex variable

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