This article discusses two new subclasses of the bi-univalent functions category ∑ in open unit disk . The primary goal is to obtain estimations coefficients and for that are within these subclasses.

In this paper, we have introduced and investigated two new subclasses of the function class Δ of bi-univalent functions defined in the open unit disk, which are associated with the generalized Hypergeometric function. Furthermore, we find estimates on the Taylor-Maclaurin coefficient | a2 | and | a3 | for the functions belonging to these new classes.

In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass. Mathematics Subject Classification: 30C45, 30C50

  , T For real numbers  and  such that 0 1      , we denote by   the class of normalized analytic functions which satisfy     Re f z     z   , T   , where denotes the open unit disk. We find some relationships involving functions in the class      . And we estimate the bounds of coefficients and solve Fekete-Szegö problem for functions in this class. Furthermore, we...

In current effort, by making use of the principle subordination, we introduce and study a new family holomorphic bi-univalent functions which are defined in open unit disk solve Fekete-Szegö problem for belong to this family.

In this study, a new class RΣμ(x,γ,α,δ,β) of bi-univalent functions studied by means Gegenbauer polynomials (GP) with Rabotnov is introduced. The coefficient the Taylor coefficients a2 and a3 Fekete-Szegö problems for belonging to have been derived as well. Furthermore, variety results will appear considering parameters in main results.

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for analytic bi-univalent function class, which call Mocanu type bi-starlike functions, related to a shell-shaped region in open unit disk complex plane. Some interesting special cases of results are also discussed.

In geometric function theory, Lucas polynomials and other special have recently gained importance. this study, we develop a new family of bi-univalent functions. Also examined coefficient inequalities Fekete-Szegö problem for via these polynomials.