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.

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>

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 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.

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

scholarly journals On Salagean type pseudo-starlike functions

2017 ◽  
Vol 21 (2) ◽  
pp. 275-285
Author(s):  
Şahsene Altınkaya ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Recent Work ◽  
Unit Disk ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Sigmoid Function ◽  
Open Unit Disk

We construct two new subclasses of univalent functions in the open unit disk U = {z : |z| < 1}. For the first class £λ(β) of Salagean type λ-pseudo-starlike functions, using the sigmoid function, we establish upper bounds for the initial coefficients of the functions in this class. Furthermore, for the second class £λ (β, φ) we obtain Fekete-Szegö inequalities. The results presented in this paper generalize the recent work of Babalola.

scholarly journals Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions

2021 ◽  
Vol 66 (4) ◽  
pp. 659-666
Author(s):  
Abbas Kareem Wanas ◽  
◽  
Agnes Orsolya Pall-Szabo ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

scholarly journals Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

2021 ◽  
Vol 39 (4) ◽  
pp. 153-164
Author(s):  
Ahmad Zireh ◽  
Saideh Hajiparvaneh
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Initial Coefficient

‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

scholarly journals Horadam polynomials and their applications tonew family of bi-univalent functions with respect to symmetric conjugate points

2020 ◽  
Vol 40 (1) ◽  
pp. 107-116
Author(s):  
Abbas Kareem Wanas ◽  
Sibel Yalçın
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Current Paper ◽  
Conjugate Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Family

In the current paper, by making use of the Horadam polynomials, we introduce and investigate a new family of holomorphic and biunivalent functions with respect to symmetric conjugate points defined in the open unit disk D. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this family.

scholarly journals Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

2021 ◽  
Vol 39 (2) ◽  
pp. 87-104
Author(s):  
Ebrahim Analouei Adegani ◽  
Ahmad Zireh ◽  
Mostafa Jafari
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In this work, we introduce a new subclas of bi-univalent functions which is defined by Hadamard product andsubordination in the open unit disk. and find upper bounds for the second and third coefficients for functions in this new subclass. Further, we generalize and improve some of the previously published results.

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