scholarly journals Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1888
Author(s):  
S. Melike Aydoğan ◽  
Zeliha Karahüseyin
Keyword(s):  
Univalent Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Coefficient Bounds ◽  
Special Cases

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

scholarly journals INITIAL COEFFICIENT BOUNDS FOR CERTAIN CLASSES OF MEROMORPHIC BI-UNIVALENT FUNCTIONS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450005 ◽  
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Initial Coefficient ◽  
Coefficient Problems ◽  
Appl Math

In 2010, Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(10) (2010) 1188–1192] reviewed the study of coefficient problems for bi-univalent functions. Inspired by the pioneering work of Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(10) (2010) 1188–1192], there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(10) (2010) 1188–1192] and Halim et al. [Coefficient estimates for meromorphic bi-univalent functions, preprint (2011), arXiv:1108.4089], in this paper, we propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the coefficients |b0| and |b1| for functions in these new classes. Some interesting remarks of the results presented here are also discussed.

scholarly journals Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

2021 ◽  
Vol 25 (1) ◽  
pp. 71-80
Author(s):  
Serap Bulut ◽  
Wanas Kareem
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Special Cases

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

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1(Suppl.)) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

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 Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

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.

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 Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 548
Author(s):  
Lina Ma ◽  
Shuhai Li ◽  
Xiaomeng Niu
Keyword(s):  
Harmonic Function ◽  
Univalent Functions ◽  
Harmonic Mapping ◽  
Conjugate Points ◽  
Original Research ◽  
Coefficient Estimates ◽  
Covering Theorem ◽  
Geometric Properties ◽  
Distortion Estimates ◽  
First Time

In the paper, we introduce some subclasses of harmonic mapping, the analytic part of which is related to general starlike (or convex) functions with a symmetric conjecture point defined by subordination. Using the conditions satisfied by the analytic part, we obtain the integral expressions, the coefficient estimates, distortion estimates and the growth estimates of the co-analytic part g, and Jacobian estimates, the growth estimates and covering theorem of the harmonic function f. Through the above research, the geometric properties of the classes are obtained. In particular, we draw figures of extremum functions to better reflect the geometric properties of the classes. For the first time, we introduce and obtain the properties of harmonic univalent functions with respect to symmetric conjugate points. The conclusion of this paper extends the original research.

scholarly journals Coefficient estimates for some subclasses of bi-univalent functions related to m-fold symmetry

2019 ◽  
Vol 11 (2) ◽  
pp. 81-86
Author(s):  
Waggas Galib Atshan ◽  
Salwa Kalf Kazim
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Special Cases

The purpose of present paper is to introduce and  investigate two new subclasses    and  of analytic and m-fold symmetric bi- univalent functions in the  open unit disk . Among other results belonging to these subclasses upper coefficients bounds   and  are obtained in this study. Certain special cases are also indicated .  

scholarly journals Coefficient Estimates of Some Classes of Univalent Functions using Subordination Principle

2020 ◽  
pp. 1-11
Author(s):  
Olubunmi A. Fadipe-Joseph ◽  
E. A. Aina ◽  
E. O. Titiloye
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Hankel Determinants ◽  
Coefficient Bounds

In this work, two classes T(b, λ) and V(b, λ) were defined. Coefficient bounds, Fekete-Szegö functional and Hankel determinants for the classes were obtained. The results obtained generalized some earlier ones.

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