Pascal distribution series and its applications on parabolic starlike functions with positive coefficients

Gangadharan, Murugusundaramoorthy

doi:10.22075/ijnaa.2020.20323.2146

Pascal distribution series and its applications on parabolic starlike functions with positive coefficients

Document Type : Research Paper

Author

Murugusundaramoorthy Gangadharan

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Deemed to be University, Vellore-632 014, India

10.22075/ijnaa.2020.20323.2146

Abstract

The purpose of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. To be more precise, we investigate such connections with the classes of parabolic starlike and uniformly convex functions with positive coefficients in the open unit disk $\mathbb{U}.$

Keywords

Starlike functions

Convex functions

Uniformly Starlike functions

Uniformly Convex functions

Hadamard product

Pascal distribution series