Initial coefficient estimates for certain subclasses of bi-univalent functions of Ma-Minda type

2015 ◽  
Vol 9 ◽  
pp. 2299-2308 ◽  
Author(s):  
C. Ramachandran ◽  
R. Ambrose Prabhu ◽  
N. Magesh
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Initial Coefficient

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 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 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 Special Subfamilies of Holomorphic and Bi-univalent Functions related to Quasi-subordination

2021 ◽  
pp. 225-237
Author(s):  
S. R. Swamy ◽  
Y. Sailaja
Keyword(s):  
Univalent Functions ◽  
Current Work ◽  
Coefficient Estimates ◽  
Initial Coefficient

In the current work, special subfamilies of holomorphic bi-univalent functions based on quasi-subordination are introduced. Initial coefficient estimates for functions belonging to these subfamilies are established. Several consequences of our results and connections to known families are indicated.

scholarly journals Coefficient Estimates for Generalized Analytic Bi-Univalent Functions

2019 ◽  
pp. 173-178
Author(s):  
Deborah Olufunmilayo Makinde
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Initial Coefficient

For the normalized analytic functions of the form..... .We obtain the initial coefficient estimates for the subclassThe relationship with some coefficient estimates in the literature with that of the subclass above was also considered.

scholarly journals Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (p − q)-Wanas Operator

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2118
Author(s):  
Abbas Kareem Wanas ◽  
Luminiţa-Ioana Cotîrlǎ
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Function Theory ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Geometric Function Theory ◽  
Coefficient Estimates ◽  
Quantum Calculus ◽  
Initial Coefficient ◽  
Geometric Function

The motivation of the present article is to define the (p−q)-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) and SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined in the unit disk U associated with the (p−q)-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters.

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