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.

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.

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 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 Initial Coefficients of Biunivalent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

scholarly journals Initial coefficient estimates for a classes of m-fold symmetric bi-univalent functions involving Mittag-Leffler function

2020 ◽  
Vol 24 (2) ◽  
pp. 51-61
Author(s):  
Abbas Wanas ◽  
Huo Tang
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Initial Coefficient ◽  
Special Cases

The main object of the present paper is to use Mittag-Leffler function to introduce and study two new classes RSm(g, l, e, d, t ; a) and R * Sm(g, l, e, d, t ; b) of Sm consisting of analytic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Also, we determine the estimates on the initial coefficients |am+1| and |a2m+1| for functions in each of these new classes. Furthermore, we indicate certain special cases for our results.

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