In this paper, subclasses of the function class ∑ analytic and bi-univalent functions associated with operator L_q^(k, λ) are introduced defined in open unit disk △ by applying quasi-subordination. We obtain some results about corresponding bound estimations coefficients a_(2 ) a_(3 ).

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass ( ) , Σ ψ λ of analytic and bi-univalent functions defined in the open unit disc  . Further, we find estimates on the coefficients 2 a and 3 a for functions in this subclass. Many relevant connections with known or new results are pointed out.

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.

For the first time, we attempted to define two new sub-classes of bi-univalent functions in open unit disc complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients these classes were obtained. Moreover, also determined Fekete–Szegö inequalities for function and several related corollaries.

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.