scholarly journals Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials

2021 ◽  
Vol 20 ◽  
pp. 121-134
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Upper Bounds ◽  
Current Work ◽  
Series Expansions ◽  
Maclaurin Series ◽  
Coefficient Bounds ◽  
Lucas Polynomials ◽  
Special Cases

In the current work, we use the (M,N)-Lucas Polynomials to introduce a new families of holomorphic and bi-Prestarlike functions defined in the unit disk O and establish upper bounds for the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we debate Fekete-Szeg¨o problem for thesefamilies. Further, we point out several certain special cases for our results.

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 Coefficient Bounds and Fekete-Szegӧ Problem for a New Subclasses of Holomorphic Bi-Univalent Functions Defined by Horadam polynomials

2021 ◽  
Vol 26 (2) ◽  
pp. 52-65
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, by making use the Horadam polynomials, we introduce and investigate two new subclasses  and  of the function class  of holomorphic bi-univalent functions in the open unit disk Δ. For functions belonging to this subclasses, we obtain upper bounds for the second and third coefficients and discuss Fekete-Szegӧ problem. Furthermore, we point out several new special cases of 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.

Coefficient bounds for certain families of bi-univalent functions defined by Wanas operator

2021 ◽  
pp. 2250100
Author(s):  
Abbas Karem Wanas ◽  
Aqeel Ketab Al-Khafaji
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Bounds ◽  
Special Cases

The main purpose of this paper is to find upper bounds for the second and third Taylor–Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Wanas operator. Further, we point out certain special cases for our results.

scholarly journals Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator

2021 ◽  
Vol 5 (1) ◽  
pp. 42-50
Author(s):  
Timilehin Gideon Shaba ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Special Cases

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

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

2021 ◽  
Vol 20 ◽  
pp. 105-114
Author(s):  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds

\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.    

scholarly journals Coefficient bounds for new subclasses of bi-univalent functions

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1165-1171 ◽  
Author(s):  
Murat Cağlar ◽  
Halit Orhan ◽  
Nihat Yağmur
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds

In the present investigation, we consider two new subclasses N?? (?, ?) and N?? (?, ?) of bi?univalent functions defined in the open unit disk u = {z : |z| < 1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.

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.

Behavior of Coefficients of Inverses of α-Spiral Functions

1986 ◽  
Vol 38 (6) ◽  
pp. 1329-1337 ◽  
Author(s):  
Richard J. Libera ◽  
Eligiusz J. Złotkiewicz
Keyword(s):  
Unit Disk ◽  
Series Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Maclaurin Series ◽  
Koebe Function ◽  
One To One ◽  
Image Position

If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form(1.1)then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.(1.1)serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .

scholarly journals Subclasses of close-to-convex functions

1983 ◽  
Vol 6 (3) ◽  
pp. 449-458 ◽  
Author(s):  
E. M. Silvia
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Integral Operators ◽  
Coefficient Bounds ◽  
Class Of Functions

Let𝒦[C,D],−1≤D<C≤1, denote the class of functionsg(z),g(0)=g′(0)−1=0, analytic in the unit diskU={z:|z|<1}such that1+(zg″(z)/g′(z))is subordinate to(1+Cz)/(1+Dz),z ϵ U. We investigate the subclasses of close-to-convex functionsf(z),f(0)=f′(0)−1=0, for which there existsg ϵ 𝒦[C,D]such thatf′/g′is subordinate to(1+Az)/(1+Bz),−1≤B<A≤1. Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.

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