A certain family of bi-univalent functions associated with the Pascal distribution series based upon the Horadam polynomials

Abstract

The purpose of this article is to introduce a new subclass ℋΣ(δ,λ,m,θ,x) of analytic and bi-univalent functions by using the Horadam polynomials, which is associated with the Pascal distribution series and to investigate the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szegö inequality for functions in the class ℋΣ(δ,λ,m,θ,x) which we have introduced here.

Keywords

• analytic functions
• univalent functions
• bi-univalent functions
• horadam polynomials
• upper bounds
• fekete-szegö problem
• pascal distribution series
• subordination between analytic functions