Certain Results on Starlike and Close-to-Convex Functions

Document Type : Original Article

Authors

Pardeep Kaur ¹

Sukhwinder Singh Billing ²

¹ Department of Applied Sciences, Baba Banda Singh Bahadur Engineering College, Fatehgarh Sahib-140407, Punjab, India.

² Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.

10.22034/kjm.2019.84141

Abstract

Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and close-to-convex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and close-to-convexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.

Keywords

Starlike function

close-to-convex function

Bazilevič function

differential subordination

Subjects

• 30 Functions of a complex variable

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