In this article we introduce three new subclasses of the class bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using subordinations with whose coefficients are Gregory numbers. First, evidence that these classes not empty, i.e., they contain other besides identity one. For in each function classes, investigate estimates a2 a3 Taylor–Maclaurin Fekete–Szegő functional problems. The mai...

The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For in constructed class, explore estimates Taylor–Maclaurin coefficients a2 a3, next, solve Fekete–Szegő functional problem. A number interesting result...

In the present paper, a general subclass Mh,p ?m (?, ?) of m-Fold symmetric bi-univalent functions is de?ned. Also, estimates TaylorMaclaurin coefficients |am+1|, |a2m+1| and Fekete-Szegö problems are obtained for in this new subclass. The results presented paper would generalize improve some recent works several earlier authors.