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

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