scholarly journals Faber polynomial coefficients estimates for certain subclasses of $ q $-Mittag-Leffler-Type analytic and bi-univalent functions

2021 ◽  
Vol 7 (2) ◽  
pp. 2512-2528
Author(s):  
Zeya Jia ◽  
◽  
Nazar Khan ◽  
Shahid Khan ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
Polynomial Coefficients ◽  
Polynomial Expansion Method ◽  
Generalized Differential

<abstract><p>In this paper, we introduce the $ q $-analogus of generalized differential operator involving $ q $-Mittag-Leffler function in open unit disk</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} E = \left \{ z:z\in \mathbb{C\ \ }\text{ and} \ \ \left \vert z\right \vert &lt;1\right \} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>and define new subclass of analytic and bi-univalent functions. By applying the Faber polynomial expansion method, we then determined general coefficient bounds $ |a_{n}| $, for $ n\geq 3 $. We also highlight some known consequences of our main results.</p></abstract>

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

Estimates on Initial Coefficients of Certain Subclasses of Bi-Univalent Functions Associated with Al-Oboudi Differential Operator

2017 ◽  
Vol 84 (1-2) ◽  
pp. 73
Author(s):  
Amol B. Patil ◽  
Uday H. Naik
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation we introduce two subclasses Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> [η, α, λ] and Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> (η, β, λ) of the function class Σ of bi-univalent functions defined in the open unit disk. These subclasses are defined by using the Al-Oboudi differential operator, which is the generalized Salagean's differential operator. Also we find estimates on initial coeffcients |a<sub>2</sub>| and |a<sub>3</sub>| for the functions in these subclasses and consider some related subclasses in connection with these subclasses.

scholarly journals Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hameed Ur Rehman ◽  
Maslina Darus ◽  
Jamal Salah
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Positive Real Part ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Faber Polynomial ◽  
Coefficient Problems

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

scholarly journals Coefficient bounds for a certain class of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1839-1845 ◽  
Author(s):  
H.M. Srivastava ◽  
Sevtap Eker ◽  
Rosihan Alic
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
Recent Developments ◽  
Polynomial Expansions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

2018 ◽  
Vol 68 (2) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmad Zireh ◽  
Ebrahim Analouei Adegani ◽  
Mahmood Bidkham
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Polynomial Coefficient ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Faber Polynomial

Abstract In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes $\begin{array}{} H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h) \end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

scholarly journals Symmetric Conformable Fractional Derivative of Complex Variables

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 363 ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Rafida M. Elobaid ◽  
Suzan J. Obaiys
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Unit Disk ◽  
Analytic Functions ◽  
Differential Operators ◽  
Function Theory ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Symmetric Differential Operators

It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose of this effort is to provide a study of SCDO connected with the geometric function theory. These differential operators indicate a generalization of well known differential operator including the Sàlàgean differential operator. Our contribution is to impose two classes of symmetric differential operators in the open unit disk and to describe the further development of these operators by introducing convex linear symmetric operators. In addition, by acting these SCDOs on the class of univalent functions, we display a set of sub-classes of analytic functions having geometric representation, such as starlikeness and convexity properties. Investigations in this direction lead to some applications in the univalent function theory of well known formulas, by defining and studying some sub-classes of analytic functions type Janowski function and convolution structures. Moreover, by using the SCDO, we introduce a generalized class of Briot–Bouquet differential equations to introduce, what is called the symmetric conformable Briot–Bouquet differential equations. We shall show that the upper bound of this class is symmetric in the open unit disk.

scholarly journals Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

scholarly journals Coefficient Estimates for Initial Taylor-Maclaurin Coefficients for a Subclass of Analytic and Bi-Univalent Functions Defined by Al-Oboudi Differential Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

We introduce and investigate an interesting subclass𝒩𝒫Σλ,δ(n,β;h)of analytic and bi-univalent functions in the open unit disk𝕌. For functions belonging to the class𝒩𝒫Σλ,δ(n,β;h), we obtain estimates on the first two Taylor-Maclaurin coefficientsa2anda3.

scholarly journals Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Saqib Hussain ◽  
Shahid Khan ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus ◽  
Zahid Shareef
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Initial Coefficient ◽  
Polynomial Expansions

We introduce in our present investigation a new subclass of analytic and biunivalent functions associated with Ruscheweyh q-differential operator in open unit disk E. We use the Faber polynomial expansions to find nth coefficients bounds of class of bisubordinate functions and also find initial coefficient estimates.

scholarly journals On a Subclass of Analytic and Univalent Functions with Positive Coefficients Defined by a Differential Operator

2021 ◽  
pp. 2000-2008
Author(s):  
Aqeel Ketab Al-khafaji
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Positive Coefficients ◽  
Analytic And Univalent Functions

In this paper, a differential operator is used to generate a subclass of analytic and univalent functions with positive coefficients. The studied class of the functions includes:     which is defined in the open unit disk  satisfying the following condition This leads to the study of properties such as coefficient bounds, Hadamard product, radius of close –to- convexity, inclusive properties, and (n, τ) –neighborhoods for functions belonging to our class.

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