The paper introduces a new family of analytic bi-univalent functions that are injective and possess inverses, by employing q-analogue the derivative operator. Moreover, article establishes upper bounds Taylor–Maclaurin coefficients these functions, which can aid in approximating accuracy approximations using finite number terms. obtained Faber polynomial expansions. These apply to both initial ...

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.

In current manuscript, using Laguerre polynomials and (p−q)-Wanas operator, we identify upper bounds a2 a3 which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes W∑(η,δ,λ,σ,θ,α,β,p,q;h) K∑(ξ,ρ,σ,θ,α,β,p,q;h) cover the convex starlike functions. Also, discuss Fekete-Szegö type inequality defined class.

In the current work, we use (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve linear combination between Bazilevic ?-pseudo-starlike function defined in unit disk D establish upper bounds for second third coefficients belongs this family. Also, discuss Fekete-Szeg? problem

By making use of $q$-derivative and $q$-integral operators, we define a class analytic bi-univalent functions in the unit disk $|z|<1$. Subsequently, investigate some properties such as early coefficient estimates then obtain Fekete-Szeg\"o inequality for both real complex parameters. Further, interesting corollaries are discussed.

In this paper, we investigate a new subclass ?n?(?,?,?)of analytic and bi-univalent functions in the open unit disk U ={z:|z|<1} defined by Al-Oboudi differential operator. We obtain coefficient bounds for belonging to ?n?(?,?,?). Relevant connections of results presented here with various well-known are briefly indicated.