In this work, we introduce and investigate a new subclass of analytic bi-univalent functions based on subordination conditions between the zero-truncated Poisson distribution Gegenbauer polynomials. More precisely, will estimate first two initial Taylor–Maclaurin coefficients solve Fekete–Szegö functional problem for belonging to subclass.

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ ,γ ;φ), H S Σ(α), RΣ(η ,γ ;φ) and BΣ(μ ;φ) (0 λ 1; γ ∈ C {0}; α ∈ C; 0 η < 1; μ 0) of bi-univalent functions, φ is an analytic function with positive real part in the unit disk D, satisfying φ(0) = 1, φ ′(0) > 0, and φ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylo...

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z?C:z&lt;1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 Fekete–Szegö inequalities a3??a22 these subclasses.

The purpose of this article is to introduce a new subclass analytic and bi-univalent functions, in associated with sigmoid function investigate the upper bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Further we obtain Fekete-Szego inequalities class sigma. We also give several illustrative examples functionclass which here.

In this article, we aim to describe a new operator J_(s,a,μ)^(δ,λ) via convolution. Moreover, present subclass C_Σm (τ;β) related m-fold symmetric bi-univalent functions in the open unit disk Θ={z∈C∶|z| ˂ 1 }. Finally, an estimate Hankel determinant for are given.

Motivated by q-calculus, we define a new family of Σ, which is the bi-univalent analytic functions in open unit disc U that related to Einstein function E(z). We establish estimates for first two Taylor–Maclaurin coefficients |a2|, |a3|, and Fekete–Szegö inequality a3−μa22 belong these families.