New Subclass Of Bi-univalent Functions Research Articles

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.

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

In this paper, two new subclasses of bi-univalent functions are introduced by using generalized Bivariate Fibonacci polynomials. First, initial Taylor–Maclaurin coefficient estimates are determined for these new subclasses and then, the famous Fekete–Szegö problem is investigated for the functions belonging to these new subclasses. Finally, for the some special values of parameters several corollaries are presented.

Fekete-Szego inequality of bi-starlike and bi-convex functions of order b associated with symmetric q-derivative in conic domains

"In this paper, two new subclasses of bi-univalent functions related to conic domains are de ned by making use of symmetric q-di erential operator. The initial bounds for Fekete-Szego inequality for the functions f in these classes are estimated."

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.

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.

New Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers

Abstract In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses D n,ρ Σ, δ (Φ) and F n,α Σ, δ (Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |a 2| and |a 3| of the bi-univalent function subclasses.

Coefficient inequalities for new subclasses of bi-univalent functions defined by using the function fδ

In this investigation, we introduce and study two new subclasses of bi-univalent functions defined by using the function [Formula: see text] and Salagean differential operator. Furthermore, we find estimates on the coefficients [Formula: see text] and [Formula: see text] for these function classes.

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.

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.

Faber Polynomial Expansion for a New Subclass of Bi-univalent Functions Endowed with $(p,q)$ Calculus Operators

In this paper, we use the Faber polynomial expansion techniques to get the general Taylor-Maclaurin coefficient estimates for $|a_n|,\ (n\geq 4)$ of a generalized class of bi-univalent functions by means of $(p,q)-$calculus, which was introduced by Chakrabarti and Jagannathan. For functions in such a class, we get the initial coefficient estimates for $|a_2|$ and $|a_3|.$ In particular, the results in this paper generalize or improve (in certain cases) the corresponding results obtained by recent researchers.

Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

Hankel Inequalities for a Subclass of Bi-Univalent Functions based on Salagean type q-Difference Operator

In this investigation a new subclass of bi-univalent functions is established that is defined in the open unit disk Δ={ 𐌶 ∈ ℂ: |𐌶| < 1} and are endowed with the Salagean type q -difference operator. Then, Hankel inequalities for the new function class are obtained and several related consequences of the results are also stated.

On some new subclass of bi-univalent functions associated with the Opoola differential operator

On some new subclass of bi-univalent functions associated with the Opoola differential operator

Maclaurin Coefficient Estimates for New Subclasses of Bi-univalent Functions Connected with aq-Analogue of Bessel Function

In this paper, we introduce new subclasses of the function classΣof bi-univalent functions connected with aq-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficientsa2anda3for functions in these new subclasses.

New subclasses bi-univalent functions related to shell-like curves involving hypergeometric functions

In the present paper, new subclasses of bi-univalent functions of complex order associated with hypergeometric functions are introduced and coefficient estimates for functions in these classes are obtained. Several new (or known) consequences of the results are also pointed out.