New Subclass 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.

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

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.

Fekete-Szegö Inequality for a Subclass of Bi-univalent Functions by Applying Sălăgean q-Differential Operator

Throughout this study, we propose a new subclass of bi-univalent functions by applying Sălăgean q-differential operator and denoted as LΣ_q^k (λ,ϕ). Further, we acquired the values of the initial coefficients |a_2 | and |a_3 | for functions f∈LΣ_q^k (λ,ϕ) which yield to this study’s preliminary result. Subsequently, the preliminary result was applied to obtain the upper bound of Fekete-Szegö inequality, |a_3-ρa_2^2 |, for functions f∈LΣ_q^k (λ,ϕ).

New subclasses of bi-univalent functions connected with a q-analogue of convolution based upon the Legendre polynomials

"In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-analogue of convolution by using the Legendre polynomials. Furthermore, we find estimates on the fi rst two Taylor-Maclaurin coef cients |a_2| and |a_2| for functions in these subclasses and obtain Fekete-Szego problem for these subclasses."

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass.

Generalized bivariate Fibonacci polynomial and two new subclasses of bi-univalent functions

This paper deals with two new subclasses of holomorphic and bi-univalent functions in the open unit disk defined by generalized bivariate Fibonacci polynomials. In this paper the coefficient bounds are estimated for [Formula: see text] and [Formula: see text] which [Formula: see text] and [Formula: see text] are the Taylor–Maclaurin coefficients of the functions belonging to these new subclasses. Then, the Fekete–Szegö problem is handled for the functions in these subclasses. Also, several remarks are presented. The results of this paper generalize certain earlier results in the literature.

Second Hankel Determinant for a New Subclass of Bi-Univalent Functions Related to the Hohlov Operator

A new subclass of bi-univalent functions associated with the Hohlov operator is introduced. Certain properties such as the coefficient bounds, Fekete-Szegö inequality and the second Hankel determinant for functions in the subclass are obtained. In particular, several known results are generalized.

Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers

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

A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials

In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in the symmetry domain U defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete–Szegö functional problems and the Taylor–Maclaurin coefficients a2 and a3 for the functions that belong to each of these new subclasses of the bi-univalent function classes. Some more results are revealed after concentrating on the parameters employed in our main results.

A New Subclass of Bi-Univalent Functions Defined by a Certain Integral Operator

We introduce a comprehensive subfamily of analytic and bi-univalent functions in this study using Horadam polynomials and the q-analog of the Noor integral operator. We establish upper bounds for the absolute values of the second and the third coefficients and the Fekete–Szegö functional for the functions belonging to this family. Various observations of the results presented here are also discussed.

Coefficient Estimates of New Families of Analytic Functions Associated with q-Hermite Polynomials

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients υ2, υ3, and υ4 of the Taylor–Maclaurin series and that of the Fekete–Szegö functional associated with the new classes, and we give the many consequences of our findings.

Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation

<abstract><p>In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szegö inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature.</p></abstract>

On a new subclass of biunivalent functions associated with the $(p,q)$-Lucas polynomials and bi-Bazilevic type functions of order $\rho+i\xi$

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented.

New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z∈C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 and Fekete–Szegö inequalities a3−μa22 for these new subclasses.

Coefficient Estimates for Some Classes of Biunivalent Function Associated with Jackson q -Difference Operator

Using the Jackson q -difference operator, we present two new subclasses of biunivalent functions. Furthermore, we estimate the initial Taylor-Maclaurin coefficients a 2 and a 3 of functions belonging to these new subclasses. Our results generalize some of the previously related works of several authors.

Correction to: On some new subclasses of bi-univalent functions defined by generalized Bivariate Fibonacci polynomial

Correction to: On some new subclasses of bi-univalent functions defined by generalized Bivariate Fibonacci polynomial

Fekete–Szegö Inequalities for a New Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

We introduce and investigate in this paper a new subclass of bi-univalent functions associated with the Gegenbauer polynomials which satisfy subordination conditions defined in a symmetric domain, which is the open unit disc. For this new subclass, we obtain estimates for the Taylor–Maclaurin coefficients a2,a3 and the Fekete–Szegö inequality a3−μa22.

Applications of q-Hermite Polynomials to Subclasses of Analytic and Bi-Univalent Functions

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaining traction in current fields, including computational fluid dynamics, computational probability, data assimilation, statistics, numerical analysis, and image and signal processing. In this paper, using q-Hermite polynomials, we define a new subclass of bi-univalent functions. We then obtain a number of important results such as bonds for the initial coefficients of |a2|, |a3|, and |a4|, results related to Fekete–Szegö functional, and the upper bounds of the second Hankel determinant for our defined functions class.

Bounds For the Coefficients of Two New Subclasses of Bi-Univalent Functions

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