A General and Comprehensive Subclass of Univalent Functions Associated with Certain Geometric Functions

Abstract

In this paper, taking into account the intriguing recent results of Rabotnov functions, Poisson functions, Bessel functions and Wright functions, we consider a new comprehensive subclass Oμ(Δ1,Δ2,Δ3,Δ4) of univalent functions defined in the unit disk Λ={τ∈C:τ1}. More specifically, we investigate some sufficient conditions for Rabotnov functions, Poisson functions, Bessel functions and Wright functions to be in this subclass. Some corollaries of our main results are given. The novelty and the advantage of this research could inspire researchers of further studies to find new sufficient conditions to be in the subclass Oμ(Δ1,Δ2,Δ3,Δ4) not only for the aforementioned special functions but for different types of special functions, especially for hypergeometric functions, Dini functions, Sturve functions and others.

Keywords

• analytic functions
• Rabotnov function
• Poisson distribution
• Bessel function
• Wright function