SOME CONDITIONS FOR FUNCTIONS DEFINED BY BINOMIAL DISTRIBUTION TO BE IN A COMPREHENSIVE SUBFAMILY OF ANALYTIC FUNCTIONS

Abstract

In this paper, considering the exciting recent results on binomial distribution,we examine an extensive subfamily Θϖ(C1,C2,C3,C4) of univalent functions. Also, we givesome conditions for the functions F(β,δ,ℷ), F(β,δ,ℷ)h and the operator L(β,δ,ℷ) dened bythe binomial distribution to be in this subfamily. The novelty of this research to inspire researchers of further studies to find new conditions to be in the subfamily Θϖ(C1,C2,C3,C4) not only for binomial distribution but also for many other special functions. Moreover, we summarizes many previous studies.