On Subclasses of Uniformly Convex Spriallike Function Associated with Poisson Distribution Series

Abstract

Geometric Function Theory is one of the major area of mathematics which suggests the significance of geometric ideas and problems in complex analysis. Recently, the univalent functions are given particular attention and they are used to construct linear operators that preserve the class of univalent functions and some of its subclasses. Also, similar attention has been given to distribution series. Many authors have studied about certain subclasses of univalent and bi-univalent functions connected with distribution series like Pascal distribution, Binomial distribution, Poisson distribution, Mittag-Leffler-type Poisson distribution, Geometric distribution, Exponential distribution, Borel distribution, Generalized distribution and Generalized discrete probability distribution to name few. Some of the important results on Uniformly convex spirallike functions (UCF) and Uniformly spirallike functions (USF) related with such a distribution series are also of interest. The main aim of the present investigation is to obtain the necessary and sufficient conditions for Poisson distribution series to belong to the classes <img src=image/13427077_01.gif> and <img src=image/13427077_02.gif>. The inclusion properties associated with Poisson distribution series are taken up for study in this article. Proof of some inequalities on integral function connected to Poisson distribution series has also been discussed. Further, some corollaries and results that follow consequently from the theorems are also analysed.