Polygonal Bazilevič Functions

1985 ◽  
pp. 85-90
Author(s):  
B. Case ◽  
J. Quine
Keyword(s):  
Bazilevic Functions

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.

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

scholarly journals Chebyshev Polynomials for Certain Subclass of Bazilevic Functions Associated with Ruscheweyh Derivative

2021 ◽  
Vol 45 (02) ◽  
pp. 173-180
Author(s):  
A. R. S. JUMA ◽  
S. N. AL-KHAFAJI ◽  
O. ENGEL
Keyword(s):  
Chebyshev Polynomials ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Bazilevic Functions

In this paper, through the instrument of the well-known Chebyshev polynomials and subordination, we defined a family of functions, consisting of Bazilević functions of type α, involving the Ruscheweyh derivative operator. Also, we investigate coefficient bounds and Fekete-Szegö inequalities for this class.

scholarly journals Gamma-Bazilevič Functions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 175
Author(s):  
Sa’adatul Fitri ◽  
Derek K. Thomas
Keyword(s):  
Class B ◽  
Coefficient Problems ◽  
Bazilevic Functions

For γ ≥ 0 and α ≥ 0 , we introduce the class B 1 γ ( α ) of Gamma–Bazilevič functions defined for z ∈ D by R e z f ′ ( z ) f ( z ) 1 − α z α + z f ″ ( z ) f ′ ( z ) + ( α − 1 ) z f ′ ( z ) f ( z ) − 1 γ z f ′ ( z ) f ( z ) 1 − α z α 1 − γ > 0 . We shown that B 1 γ ( α ) is a subset of B 1 ( α ) , the class of B 1 ( α ) Bazilevič functions, and is therefore univalent in D . Various coefficient problems for functions in B 1 γ ( α ) are also given.

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