In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, establish bounds initial coefficients υ2, υ3, and υ4 Taylor–Maclaurin series that Fekete–Szegö functional associated with classes, give many consequences our findings.

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By virtue Faber polynomial expansions, estimation n?th(n?3) Taylor–Maclaurin coefficients an obtained. Furthermore, bounds value first two such established.

In this paper, we introduce and investigate a new subclass of the function class Σ of biunivalent functions of the Bazilevic̆ type defined in the open unit disk, which are associated with the Hohlov operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Several (known...

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...

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

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric defined in ?={z?C:|z|<1} is introduced. The estimates for general Taylor–Maclaurin coefficients introduced are obtained by making use Faber polynomial expansions. In particular, several previous results generalized.

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.

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].