scholarly journals Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions

2021 ◽  
Author(s):  
Abdel Moneim LASHİN ◽  
Abeer BADGHAİSH ◽  
Amani BAJAMAL
Keyword(s):  
Faber Polynomials ◽  
Bazilevic Functions

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 inequalities for a subclass of Bazilevič functions

2020 ◽  
Vol 53 (1) ◽  
pp. 27-37
Author(s):  
Sa’adatul Fitri ◽  
Derek K. Thomas ◽  
Ratno Bagus Edy Wibowo ◽  
Keyword(s):  
Recent Work ◽  
Sharp Bounds ◽  
Coefficient Problems ◽  
Coefficient Inequalities ◽  
Bazilevic Functions

AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying \left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1.

Power matrices for Faber polynomials and conformal welding

2013 ◽  
Vol 58 (9) ◽  
pp. 1247-1259 ◽  
Author(s):  
Bryan Penfound ◽  
Eric Schippers
Keyword(s):  
Faber Polynomials ◽  
Conformal Welding

Completeness of subsystems of faber polynomials

2012 ◽  
Vol 56 (9) ◽  
pp. 1-4
Author(s):  
L. K. Dodunova ◽  
S. A. Savikhin
Keyword(s):  
Faber Polynomials

scholarly journals Growth results for a subclass of Bazilevič functions

1985 ◽  
Vol 8 (4) ◽  
pp. 785-793
Author(s):  
Rabha Md. El-Ashwah ◽  
D. K. Thomas
Keyword(s):  
Unit Disc ◽  
Starlike Function ◽  
Area Function ◽  
Proper Subclass ◽  
Bazilevic Functions

Forα>0, letB(α)be the class of regular normalized Bazilevič functions defined in the unit disc. Choosing the associated starlike functiong(z)≡zgives a proper subclassB1(α)ofB(α). ForB(α), correct growth estimates in terms of the area function are unknown. Several results in this direction are given forB1(12).

scholarly journals On Bazilevic functions

1987 ◽  
Vol 10 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Khalida I. Noor ◽  
Sumayya A. Al-Bany
Keyword(s):  
Unit Disc ◽  
Starlike Function ◽  
Hankel Determinant ◽  
Bazilevic Functions

LetB(β)be the class of Bazilevic functions of typeβ(β>0). A functionf ϵ B(β)if it is analytic in the unit discEandRezf′(z)f1−β(z)gβ(z)>0, wheregis a starlike function. We generalize the classB(β)by takinggto be a function of radius rotation at mostkπ(k≥2). Archlength, difference of coefficient, Hankel determinant and some other problems are solved for this generalized class. Fork=2, we obtain some of these results for the classB(β)of Bazilevic functions of typeβ.

scholarly journals The derivative of Bazilevič functions

1988 ◽  
Vol 104 (1) ◽  
pp. 235-235
Author(s):  
R. R. London ◽  
D. K. Thomas
Keyword(s):  
Bazilevic Functions
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