A study of analytic functions along with Poisson distribution

Abstract

In this paper, we introduce some new families of analytic functions by using Hadamard product while keeping conic like domains in view. Like the area theorem, we determine sufficient conditions as well as characterizations of these functions. Furthermore, we develop a connection between Poisson distribution series whose coefficients are probabilities of some events occurring in a fixed duration of time or space under certain conditions and some subclasses of analytic functions. To be more precise, we investigate such connections with the classes of analytic functions with complex as well as non-negative coefficients by determining sufficient conditions along with characterizations of functions involving Poisson distribution and its related variants.

Keywords

• Starlike functions
• convex functions
• subordination
• 30C45
• 30C80
• 60E05