In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to involution numbers. find initial estimates Taylor–Maclaurin coefficients |a2| |a3| for functions introduced here. also obtain a Fekete–Szegö inequality class. Several consequences our results pointed out, not yet discussed as...

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].

In this paper, we introduce and investigate two new subclasses of the functions class $ Sigma $ of bi-univalent functions defined in the open unit disk, which are associated with the Aghalary-Ebadian-Wang operator. We  estimate the coefficients $|a_{2} |$ and  $|a_{3} |$ for functions in these new subclasses. Several  consequences of the result are also pointed out.

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

In this paper, we estimate the second and third Maclaurin's coefficients of certain subclass of bi-univalent functions in open unit disk defined by Caputo Fractional calculus operator and also indicate certain special cases.

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

The purpose of the present paper is to obtain the initial coefficients for normalized analytic functions f in the open unit disk U with its inverse g = f−1 belonging to the classes H σ (φ), ST n σ (α, φ), M n σ (α, φ) and L n σ(α, φ). Relevant connections of the results presented here with various known results are briefly indicated. Finally, we give an open problem for the readers. Mathematics...

This paper establishes the upper bounds for second and third coefficients of holomorphic bi-univalent functions in a family which involves Bazilevic μ-pseudo-starlike under new operator, joining neutrosophic Poisson distribution with modified Caputo’s derivative operator. We also discuss Fekete–Szego’s function problem this family. Examples are given to support our case distribution. The fields...

We defined two new subclasses of analytic bi-univalent function class Σ, in the open unit disk related with Sălăgean–Erdély–Kober operator. The bounds on initial coefficients |a2|,|a3| and |a4| for functions these Σ are investigated. Using estimates a2,a3, we also discuss Fekete-Szegö inequality results classes this paper. Relevant connections results, presented here as corollaries, not studied...