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.

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 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.

Faber polynomial coefficient estimates for a certain subclass of meromorphic bi-univalent functions

2019 ◽  
Vol 13 (04) ◽  
pp. 2050076 ◽  
Author(s):  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

In this paper, by using the Faber polynomial expansions we can find the coefficient bounds for [Formula: see text] subclass of meromorphic bi-univalent functions. The results presented in this paper would generalize and improve some recent works.

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

scholarly journals Coefficient Estimates for Bi-univalent Functions Defined By (P, Q) Analogue of the Salagean Differential Operator Related to the Chebyshev Polynomials

2021 ◽  
Vol 53 (1) ◽  
pp. 49-66
Author(s):  
Trailokya Panigrahi ◽  
Susanta Kumar Mohapatra
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Varying Parameters ◽  
Function Classes ◽  
Sălăgean Operator ◽  
Salagean Operator

In the present investigation we use the Jackson (p,q)-differential operator to introduce the extended Salagean operator denoted by Rkp,q. Certain bi-univalent function classes based on operator Rkp,q related to the Chebyshev polynomials are introduced. First, two coefficient bounds and Fekete-Szego inequalities for the function classes are established. A number of corollaries are developed by varying parameters involved.

scholarly journals Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1567-1575 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor-Maclaurin coecients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

Coefficient estimates for a new subclass of bi-univalent functions defined by convolution

2018 ◽  
Vol 27 (1) ◽  
pp. 89-94
Author(s):  
Tuǧba Yavuz ◽  
Keyword(s):  
Univalent Function ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds

In this paper we introduce general subclasses of bi-univalent functions by using convolution. Bounds for the first two coefficients |a2| and |a3| for bi-univalent functions in these classes are obtained. The obtained results generalize the results which are given in [Murugusundaramoorthy, G., Magesh, M., Prameela, V., Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., (2013), Art. ID 573017, 3 pp.] and [Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Studia Univ. Babes¸ Bolyai Math., 31 (1986), No. 2, 70–77].

Hankel determinants of second and third order for the class 𝓢 of univalent functions

2021 ◽  
Vol 71 (3) ◽  
pp. 649-654
Author(s):  
Milutin Obradović ◽  
Nikola Tuneski
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Third Order ◽  
Hankel Determinants

Abstract In this paper we give the upper bounds of the Hankel determinants of the second and third order for the class 𝓢 of univalent functions in the unit disc.

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