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 an interesting subclass B Σ of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class B Σ we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent work of Brannan and Taha [1]. AMS Mathematics Subject Classif...

By using the q-derivative operator and Legendre polynomials, some new subclasses of q-starlike functions bi-univalent are introduced. Several coefficient estimates Fekete–Szegö-type inequalities for in each these obtained. The results derived this article shown to extend generalize those earlier works.

In the present paper, we introduce and study two new subclasses of analytic $m$-fold symmetric bi-univalent functions defined in open unit disk $U$. Furthermore, for each introduced here, obtain upper bounds initial coefficients $\left| a_{m+1}\right|$ a_{2m+1}\right|$. Also, indicate certain special cases our results.

FMN and flavodoxin, when reduced by the action of ferredoxin-TPN+ oxidoreductase, have been shown to cause both univalent and divalent reductions of oxygen. Superoxide radicals, so generated, were detected by their abilities to oxidize epinephrine to adrenochrome and to reduce cytochrome c. Superoxide dismutase inhibited these actions of the superoxide radical. The ratio of the univalent reduct...

The present paper introduces a new class of bi-univalent functions defined on symmetric domain using Gegenbauer polynomials. For in this class, we have derived the estimates Taylor–Maclaurin coefficients, a2 and a3, Fekete-Szegö functional. Several results follow upon specializing parameters involved our main results.

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.

Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson Borel Mittag-Leffler-type Miller–Ross-Type Distribution. In present paper, making use Bell we introduce investigate a new family GΣt(x,p,q,λ,β,γ) normalized functions in open unit disk U, which are associated with Horadam polyn...

In this article, we introduce and study a new family P?(?,?,k,?,?,?,r) of normalized analytic ?-pseudo-starlike bi-univalent functions by using the Horadam polynomials, which is associated with certain convolution operator defined in open unit disk U. We establish bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Furthermore, obtain Fekete-Szeg? inequality class P? (...