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Applications on a subclass of $β$ $β$ -uniformly starlike functions connected with $q$ $q$ -Borel distribution

Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah, Saudi Arabia

Corresponding author.

Present address:Department of Mathematics, College of Science and Arts, Al-Badaya,Qassim University, Qassim, Saudi Arabia

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and

G. Murugusundaramoorthy

Department of Mathematics, School of Advanced Sciences, Vellore Institute Technology, Vellore 632014, India

E-mail Address: gmsmoorthy@yahoo.com

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https://doi.org/10.1142/S1793557122501583Cited by:6 (Source: Crossref)

Abstract

The aim of this paper is to define the operator of $q$ $q$ -derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of $β$ $β$ -uniformly starlike functions $β$ $β$ - $𝒮 (α, q, λ, δ) .$ Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions $f \in β$ - $𝒮 (α, q, λ, δ) .$ We also determine the second Hankel inequality for functions belonging to this subclass.

Communicated by B. W. Schulze

Keywords:

AMSC: 05A30, 30C45, 11B65, 47B38

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