Recently, q-analogue of Noor integral operator and other special operators became importance in the field Geometric Function Theory. In this study, by connecting principle subordination we introduced an interesting class bi-univalent functions obtained coefficient estimates for new class.

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.

The aim of the present article is to introduce and investigate a new family LΣ(δ,η,θ,t;h) normalized holomorphic bi-univalent functions that involve Sakaguchi-type Bazilevič θ-pseudo-starlike associated with Laguerre polynomials. We obtain estimates on initial Taylor–Maclaurin coefficients Fekete–Szegö problem for in this family. Properties symmetry can be studied newly functions.

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of newly defined and class analytic bi-univalent functions associated q-derivative operator. Furthermore, find initial Taylor–Maclaurin coefficients for these function classes functions. also show that bounds are sharp. The sharp second Hankel determinant is given class.

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 the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, find estimates on first two Taylor-Maclaurin coefficients a2 a3 for in these obtain Fekete-Szegö problem subclasses.

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f−1 satisfying the conditions that zf ′(z)/f(z) and zg′(z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier kn...

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, 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 ).

let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...