Subclasses of starlike and convex functions involving Poisson distribution series

Abstract

The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise,we investigate such connections with the classes of analytic univalent functions of $$\beta $$ -starlike and $$\beta $$ -uniformly convex functions of order $$\alpha $$ in the open unit disk $${\mathbb {U}}$$ . Further we point out some consequences of our main results.