An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

Abstract

The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each of these bi-univalent function classes, we have derived and explored estimates of the Taylor coefficients a2 and a3 and Fekete-Szegö functional problems for functions belonging to these new subclasses.

Keywords

• Poisson distribution series
• Gegenbauer polynomials
• bi-univalent functions
• analytic functions
• Fekete-Szegö problem