Subclass Of Bi-univalent Functions Research Articles

An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions

The Mittag-Leffler-type Borel distribution is widely recognized and utilized as a beneficial and pertinent model across numerous applications. This study presents a new subclass of normalized analytic bi-univalent functions that combines Gegenbauer polynomials and the Mittag-Leffler-type Borel distribution. Employing this subclass enables us to derive novel approximations for Taylor-Maclaurin coefficients, |a2| and |a3|, as well as delve into the investigation of the Fekete-Szegö functional. Additionally, we explore a variety of new findings that arise through the specialization of parameters in our primary results.

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

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.

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.

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>

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.

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.

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 bounds and Fekete–Szegö problem for qualitative subclass of bi-univalent functions

Coefficient bounds and Fekete–Szegö problem for qualitative subclass of bi-univalent functions

Application of Gegenbauer polynomials for biunivalent functions defined by subordination

We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert $ and $% \left \vert b_{1}\right \vert $ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert $ for this subclass is obtained. We also point out some consequences of results.

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

Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

On a subclass of bi-univalent functions defined by convex combination of order α with the Faber polynomial expansion

On a subclass of bi-univalent functions defined by convex combination of order α with the Faber polynomial expansion

Generalized subclass of analytic bi-univalent functions defined by differential operator

The leading cause objectives and key results in this paper, we introduce new subclasses of certain family of analytic and bi-univalent functions defined by differential operators in the open unit disk U. The various results we obtain the first two Taylor-Maclaurin coefficients |a 2| and |a 3| for the subclass of bi-univalent function. Certain special cases are also specified.

Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator

The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function and . We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice . It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms. .

Coefficient Bounds for a New Subclasses of Bi-Univalent Functions Associated with Horadam Polynomials

\In this work we present and investigate three new subclasses of the function class of bi-univalent functions in the open unit disk defined by means of the Horadam polynomials. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients and . Also, we debate Fekete-Szegӧ inequality for functions belongs to these subclasses.

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.

Coefficient bounds for certain two subclasses of bi-univalent functions

<abstract> In this paper, coefficient bounds of bi-univalent functions in certain two subclasses, which are defined by subordination are estimated. Some special outcomes of the main results are also presented. Moreover, it is remarked that the given bounds improve and generalize some of the pervious results. </abstract>