Fekete-Szeg¨o Inequalities for a New Class of Bi-Univalent Functions Defined via the Mittag-Leffler Function

Fekete–Szeg˝o Inequalities for a New Class of Bi-Univalent Functions Defined via the Mittag-Leffler Function

2025-05-01

Mohammad Al-Ityan , Ala Amourah , Abdullah Alsoboh +4 more

In this paper, we introduce a new subclass of analytic functions denoted by $\mathcal{M}_{\Sigma}^{p,q} (\propto, \beta)$, where we use the subordination relationship between the Mittag-Leffler function and the $(p, q)$-derivative … In this paper, we introduce a new subclass of analytic functions denoted by $\mathcal{M}_{\Sigma}^{p,q} (\propto, \beta)$, where we use the subordination relationship between the Mittag-Leffler function and the $(p, q)$-derivative of $\mathfrak{F}(z)$ to define this new class. By employing the Taylor-Maclaurin series expansion, we focus on estimating the bounds for the coefficients $|a_2|$ and $|a_3|$. Moreover, we establish Fekete--Szeg\H{o} inequalities for functions within this class.

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

2023-10-08

Bilal Khan , Muhammad Ghaffar Khan , Timilehin Gideon Shaba

In recent years, many new subclasses of analytic and bi-univalent functions have been studied and examined from different viewpoints and prospectives.In this article, we introduce new subclass of analytic and … In recent years, many new subclasses of analytic and bi-univalent functions have been studied and examined from different viewpoints and prospectives.In this article, we introduce new subclass of analytic and bi-univalent functions based on Mittag-Leffler type Borel distribution associated with the Gegenbauer polynomials.Furthermore we obtain estimates for |a 2 | , |a 3 |, and |a 4 | coefficients and Fekete-Szeg ö inequality for this functions class.Providing specific values to parameters involved in our main results, we get some new results.

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Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination

2022-01-06

Long Pu-jun , G. Murugusundaramoorthy , Han-Qi Tang +1 more

Two quasi-subordination subclasses QΣ γ,k α,β (ϑ, ρ; φ) and MΣ γ,k α,β (τ, ϑ, ρ; φ) of the class Σ of analytic and bi-univalent functions associated with the convolution … Two quasi-subordination subclasses QΣ γ,k α,β (ϑ, ρ; φ) and MΣ γ,k α,β (τ, ϑ, ρ; φ) of the class Σ of analytic and bi-univalent functions associated with the convolution operator involving Mittag-Leffler function are introduced and investigated.Then, the corresponding bound estimates of the coefficients a 2 and a 3 are provided.Meanwhile, Fekete-Szeg ö functional inequalities for these classes are proved.Besides, some consequences and connections to all the theorems would be interpreted, which generalize and improve earlier known results.

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Applications of Borel Distribution and Mittag-Leffler Function on a Class of Bi-Univalent Functions

2025-02-14

Waleed Al-Rawashdeh

In this study, we present a novel class of bi-univalent functions that incorporates the Borel distribution and the Mittag-Leffler function within the open unit disk D. This is achieved by … In this study, we present a novel class of bi-univalent functions that incorporates the Borel distribution and the Mittag-Leffler function within the open unit disk D. This is achieved by employing the q-analog of the hyperbolic tangent function in conjunction with the Hadamard product. The primary goal is determining the initial coefficient bounds for functions that fall within this newly defined class. Additionally, we explore the classical Fekete-Szegö functional problem as it pertains to these functions. Moreover, we highlight several known corollaries that arise from specific selections of the parameters associated with this class.

Applications of Gegenbauer Polynomials for Subfamilies of Bi-Univalent Functions Involving a Borel Distribution-Type Mittag-Leffler Function

2023-03-23

Abdullah Alatawi , Maslina Darus , Badriah Alamri

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of … In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of bi-univalent functions via the principle of subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on the estimation of the coefficients |aℓ|(ℓ=2,3) and the Fekete–Szegö inequality for functions belonging to these subfamilies of bi-univalent functions. Several corollaries and implications of the findings are discussed. Overall, this study presents a new approach for constructing bi-univalent functions and provides valuable insights for further research in this area.

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Bounds on Initial Coefficients for Bi-Univalent Functions Linked to q-Analog of Le Roy-Type Mittag-Leffler Function

2024-10-25

Ala Amourah , Abdullah Alsoboh , Jamal Salah +1 more

This study introduces a new class of bi-univalent functions by incorporating the q-analog of Le Roy-type Mittag-Leffler functions alongside q-Ultraspherical polynomials. We formulate and solve the Fekete-Szegö functional problems for … This study introduces a new class of bi-univalent functions by incorporating the q-analog of Le Roy-type Mittag-Leffler functions alongside q-Ultraspherical polynomials. We formulate and solve the Fekete-Szegö functional problems for this newly defined class of functions, providing estimates for the coefficients |α2| and |α3| in their Taylor-Maclaurin series. Additionally, our investigation produces novel results by adapting the parameters in our initial discoveries.

Coefficient estimates and Fekete-Szegö results for a subclass of bi-univalent functions

2018-01-01

Nurdiana Nurali , Aini Janteng , Rashidah Omar

In this paper, subclass of bi-univalent functions of the class is introduced using subordination. For functions belonging to the subclass, the estimates on the Taylor Maclaurin coefficients are determined for … In this paper, subclass of bi-univalent functions of the class is introduced using subordination. For functions belonging to the subclass, the estimates on the Taylor Maclaurin coefficients are determined for functions belonging to the subclass. Furthermore, the upper bound of the Fekete-Szegӧ functional is also obtained.

Fekete-Szegö Inequality for a Subclass of Bi-Univalent Functions Linked to <i>q</i>-Ultraspherical Polynomials

2024-05-23

Abdullah Alsoboh , Murat Çağlar , Mucahit Buyankara

In this study, we introduce a new class of bi-univalent functions using q-Ultraspherical polynomials. We derive the Fekete and Szegö functional problems for functions in this new subclass, as well … In this study, we introduce a new class of bi-univalent functions using q-Ultraspherical polynomials. We derive the Fekete and Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes is presented by customizing the parameters employed in our initial discoveries.

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A CERTAIN SUBCLASS OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS

2024-04-30

P. Nandini , S. Latha

In the present work, we investigate a new subclass of bi-univalent functions by applying the q-derivative operator associated with Chebyshev polynomials. We find estimates for the general Taylor-Maclaurin coefficients of … In the present work, we investigate a new subclass of bi-univalent functions by applying the q-derivative operator associated with Chebyshev polynomials. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class and also obtain an estimation for the Fekete-Szeg¨o problem for this class.

Coefficient Estimates of Certain Subclasses of Bi-Bazilevic Functions Associated with Chebyshev Polynomials and Mittag-Leffler Function

2020-10-27

A. M. Gbolagade , Ibrahim Tunji Awolere

In this present investigation, the authors introduced certain subclasses of the function class $ T^{\alpha}_{\theta}(\lambda, \beta, t)$ of bi-Bazilevic univalent functions defined in the open unit disk $U$, which are … In this present investigation, the authors introduced certain subclasses of the function class $ T^{\alpha}_{\theta}(\lambda, \beta, t)$ of bi-Bazilevic univalent functions defined in the open unit disk $U$, which are associated with Chebyshev polynomials and Mittag-Leffler function. We establish the Taylor Maclaurin coefficients $\left|a_{2}\right|$, $\left|a_{3}\right|$ and $\left|a_{4}\right|$ for functions in the new subclass introduced and the Fekete-Szego problem is solved.

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Coefficient Estimates for New Subclasses of Bi-Univalent Functions Associated with Jacobi Polynomials

2024-11-01

Ala Amourah , Nidal Anakira , Jamal Salah +1 more

Our research introduces new subclasses of analytical functions that are defined by Jacobi polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific … Our research introduces new subclasses of analytical functions that are defined by Jacobi polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a2| and |a3|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings.

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Inclusive Subclasses of Bi-univalent Functions Specified by Euler Polynomials

2024-10-31

B. A. Frasin , Tariq Al-Hawary , Ala Amourah +2 more

Our research delineates novel subclasses of analytical functions using Euler polynomials. Afterwards, we estimate the Fekete -Szeg¨o functional problem and the Maclaurin coefficients for this subfamily, namely |a2| and |a3|. … Our research delineates novel subclasses of analytical functions using Euler polynomials. Afterwards, we estimate the Fekete -Szeg¨o functional problem and the Maclaurin coefficients for this subfamily, namely |a2| and |a3|. Additionally, several new results are shown to follow after specializing the parameters employed in our main results.

Coefficient Estimates for Two New Subclasses of Bi-univalent Functions Involving Laguerre Polynomials

2024-12-30

Elumalai Muthaiyan , Abbas Kareem Wanas

In this paper, we introduce two new subclasses of regular and bi-univalent functions using Laguerre polynomials. Then, we define some upper limits for the Taylor Maclaurin coefficients. In addition, the … In this paper, we introduce two new subclasses of regular and bi-univalent functions using Laguerre polynomials. Then, we define some upper limits for the Taylor Maclaurin coefficients. In addition, the Fekete-Szegö problem for the functions of the new subclasses. Finally, we provide some corollaries for certain values of parameters.

A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials

2024-10-31

Mohamed Illafe , Maisarah Haji Mohd , Feras Yousef +1 more

This paper introduces a novel subclass of bi-univalent analytic functions by utilizing a symmetric q-derivative operator in conjunction with Gegenbauer polynomials. Within this newly defined subclass, we derive bounds for … This paper introduces a novel subclass of bi-univalent analytic functions by utilizing a symmetric q-derivative operator in conjunction with Gegenbauer polynomials. Within this newly defined subclass, we derive bounds for the first two Maclaurin coefficients and address the Fekete-Szeg o problem. By varying the parameters in our results between 0 and 1, we obtain a range of new insights and rediscover some previously established results. This approach not only broadens the scope of bi-univalent function theory but also deepens the understanding of coefficient bounds and extremal problems within this context.

Coefficient Inequalities and Fekete–Szegö-Type Problems for Family of Bi-Univalent Functions

2023-09-12

Tariq Al-Hawary , Ala Amourah , Hasan Almutairi +1 more

In this study, we present a novel family of holomorphic and bi-univalent functions, denoted as EΩ(η,ε;Ϝ). We establish the coefficient bounds for this family by utilizing the generalized telephone numbers. … In this study, we present a novel family of holomorphic and bi-univalent functions, denoted as EΩ(η,ε;Ϝ). We establish the coefficient bounds for this family by utilizing the generalized telephone numbers. Additionally, we solve the Fekete–Szegö functional for functions that belong to this family within the open unit disk. Moreover, our results have several consequences.

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Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

2022-01-13

Ala Amourah , B. A. Frasin , Morad Ahmad +1 more

In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, … In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

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Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

2024-01-31

Waleed Al-Rawashdeh

In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, \alpha, \beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive … In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, \alpha, \beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this class.

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Coefficient Estimates and Fekete–Szegö Functional Inequalities for a Certain Subclass of Analytic and Bi-Univalent Functions

2022-03-24

Mohamed Illafe , Ala Amourah , Maisarah Haji Mohd

The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the … The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the Taylor–Maclaurin coefficients, a2 and a3, and the Fekete-Szegö functional. Several new results follow upon specializing the parameters involved in our main results.

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On a subclass of bi-univalent functions affiliated with bell and Gegenbauer polynomials

2025-01-21

Mohamed Illafe , Abdulmtalb Hussen , Maisarah Haji Mohd +1 more

This research paper explores the development of a novel class of analytic bi-univalent functions, leveraging the Bell polynomials along with the Gegenbauer polynomials as a fundamental component for establishing the … This research paper explores the development of a novel class of analytic bi-univalent functions, leveraging the Bell polynomials along with the Gegenbauer polynomials as a fundamental component for establishing the new subclass. Analytical techniques are employed to determine and evaluate the Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ and the Fekete-Szeg\{o} functional problem for functions belonging to the constructed class. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The conclusions drawn from this research enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

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

2023-09-29

Sheza M. El-Deeb , Bassant M. El-Matary

"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 … "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."

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Fekete-Szeg¨o Inequalities for a New Class of Bi-Univalent Functions Defined via the Mittag-Leffler Function

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