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 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 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 Fekete-Szegö inequalities associated with kth root transformation based on quasi-subordination

2017 ◽  
Vol 16 (1) ◽  
pp. 7-15
Author(s):  
Nanjundan Magesh ◽  
Jagadeesan Yamini
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Root Transformation ◽  
Coefficient Problems

AbstractRecently, Haji Mohd and Darus [1] revived the study of coefficient problems for univalent functions associated with quasi-subordination. Inspired largely by this article, we provide coefficient estimates with k-th root transform for certain subclasses of 𝒮 defined by quasi-subordination.

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.

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 Development of Novel Subclasses for Bi-Univalent Functions

2021 ◽  
Vol 16 ◽  
pp. 1-6
Author(s):  
MUNIRAH ROSSDY ◽  
RASHIDAH OMAR ◽  
SHAHARUDDIN CIK SOH
Keyword(s):  
Differential Operator ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Initial Coefficient

This manuscript presents the development of new subclasses for bi-univalent functions and the subclasses are closely related to Chebyshev polynomials having Al-Oboudi differential operator. The functions contained in the subclasses were used to account for the initial coefficient estimates of |a2| and |a3| .

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 class of meromorphic bi-univalent functions

2019 ◽  
Vol 11 (1) ◽  
pp. 234-245
Author(s):  
Ahmad Zireh ◽  
Safa Salehian
Keyword(s):  
Univalent Functions ◽  
Coefficient Bounds ◽  
Initial Coefficient

Abstract In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on Δ = {z ∈ ℂ: 1 < |z| < ∞}. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper generalize and improve some recent works.

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