Certain Subclasses Of Bi-univalent Functions Research Articles

Fekete-Szegö type functionals associated with certain subclasses of bi-univalent functions

In this article, we define and discuss some new subclasses of bi-univalent functions associated with Fibonacci numbers and shell-like curves. We estimate the first two Taylor-Maclaurin coefficients for functions belonging to these classes. We study the inequalities related with Fekete-Szegö type. Furthermore, we point out some corollaries related to existing result.

Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials

<abstract><p>In this paper, we introduced two novel subclasses of bi-univalent functions, $ \mathcal{M}_{\Sigma}(\alpha, \mathcal{B}(x, \xi)) $ and $ \mathcal{H}_{\Sigma}(\alpha, \mu, \mathcal{B}(x, \xi)) $, utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients $ \left|a_2\right| $ and $ \left|a_3\right| $, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.</p></abstract>

Taylor-Maclaurin coefficients and the Fekete-Szegö inequalities for certain subclasses of bi-univalent functions involving the Gegenbauer polynomials

Taylor-Maclaurin coefficients and the Fekete-Szegö inequalities for certain subclasses of bi-univalent functions involving the Gegenbauer polynomials

Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a2 and a3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

Initial estimates for certain subclasses of bi-univalent functions with $$\kappa $$-Fibonacci numbers

Initial estimates for certain subclasses of bi-univalent functions with $$\kappa $$-Fibonacci numbers

The second Hankel determinant problem for a certain subclass of bi-univalent functions

The second Hankel determinant problem for a certain subclass of bi-univalent functions

Coefficient estimation of certain subclass of bi-univalent functions defined by catas operator

Coefficient estimation of certain subclass of bi-univalent functions defined by catas operator

Certain Subclass of Bi-univalent Functions Defined by Sălăgean Differential Operator Related with Horadam Polynomials

The goal of this paper is to introduce and investigate a new subclass of bi-univalent functions using the Horadam polynomials and Sălăgean differential operator. Furthermore, coefficient estimates are given for and Fekete-Szegő inequalities for this subclass are obtained.

Second Hankel determinant for certain subclass of bi-univalent functions

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant for functions belonging to a subclass of bi-univalent functions in the open unit disk in the complex plane. Furthermore, the presented results in this work improve or generalize the recent works of other authors.

On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

Certain subclasses of bi-univalent functions defined by Chebyshev polynomials

In this paper , we obtain initial coefficient bounds for functions belonging to the subclass of bi-univalent functions $$ B^{\lambda }_{\Sigma }(f,g,h;t)$$ by using the Chebyshev polynomials. We find Fekete–Szego inequalities and also seek the upper bound for the second Hankel determinant for functions belonging to this subclass.

Certain subclass of bi-univalent functions associated with the Chebyshev polynomials based on q-derivative symmetric q-derivative

In this paper, we introduce new subclass Beq σB (λ, t) of bi-univalent functions by applying the Chebyshev polynomials. In the following, we obtain bounds for the initial coefficients and the Fekete-Szeg¨o inequalities for functions in this subclass. The results presented in this paper generalize the recent work of Altinkaya and Yalcın.

A certain subclass of bi-univalent functions associated with Bell numbers and $q-$Srivastava Attiya operator

In the present study, we introduced general a subclass of bi-univalent functions by using the Bell numbers and $q-$Srivastava Attiya operator. Also, we investigate coefficient estimates and famous Fekete-Szego inequality for functions belonging to this interesting class.

Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination

We investigate specific new subclasses of the function class ? of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses. Already pointed out are some documented and new implications of those findings.

A Subclass of Bi-Univalent Functions Defined by Generalized Sãlãgean Operator Related to Shell-Like Curves Connected with Fibonacci Numbers

The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients a2 and a3 and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases.

Application of quasi-subordination for certain subclasses of bi-univalent functions of complex order

Application of quasi-subordination for certain subclasses of bi-univalent functions of complex order

Certain subclasses of bi-univalent functions involving the Poisson distribution associated with Horadam polynomials

Certain subclasses of bi-univalent functions involving the Poisson distribution associated with Horadam polynomials

Estimate for initial MacLaurin coefficients of certain subclasses of bi-univalent functions of complex order associated with the Hohlov operator

Abstract In this paper, we define a new subclass of bi-univalent functions involving a Hohlov operator in the open unit disk. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |.

Certain Subclasses of Bi-Univalent Functions Associated with the Horadam Polynomials

In Geometric Function Theory, there have been many interesting and fruitful usages of a wide variety of special functions and special polynomials. Here, in this article, we propose to make use of the Horadam polynomials which are known to include, as their particular cases, such potentially useful polynomials as (for example) the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Pell–Lucas polynomials, and the Chebyshev polynomials of the second kind. We aim first at introducing a new class of bi-univalent functions defined by means of the Horadam polynomials. For functions belonging to this new bi-univalent function class, we then derive coefficient inequalities and consider the celebrated Fekete–Szego problem. We also provide relevant connections of our results with those considered in earlier investigations.

Second Hankel determinant for certain subclasses of bi-univalent functions involving Chebyshev polynomials

In this paper our purpose is to find upper bound estimate for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using Chebyshev polynomials.