Bi-Univalency of a Generalised Distribution Series Convoluted with Beta Function and Poisson Distribution Series via Bells Number

Abstract

In this study, the number of equivalence relations on a set of n elements is given by the n-th Bell number (Bn). These numbers represent all possible partitions of a set. By using Beta and Poisson distribution series we applied convolution principle in order to investigate coefficient estimates. The researchers focused on the relationship between Bell numbers and the bi-univalency of a generalized distribution series that combines the Poisson distribution series and the Beta function. To achieve the results, the initial bounds on coefficients for the specified classes of functions will be employed to derive the well-known Fekete-Szegö inequalities. These findings signify a fresh contribution to the realm of Geometric Function Theory (GFT) as there has been no existing literature that discusses the convolution involving both the Beta function and the Poisson distribution series