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 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 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.

scholarly journals On certain Bazilević functions of orderβ

1992 ◽  
Vol 15 (3) ◽  
pp. 613-616 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Alpha Beta ◽  
Bazilevic Functions

A certain classB(n,α,β)of Bazilević functions of orderβin the unit disk is introduced. The object of the present paper is to derive some properties of functions belonging to the classB(n,α,β). Our result for the classB(n,α,β)is the improvement of the theorem by N. E. Cho ([1]).

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