scholarly journals Growth and Coefficient Estimates for Uniformly Locally Univalent Functions on the Unit Disk

2002 ◽  
Vol 32 (1) ◽  
pp. 179-200 ◽  
Author(s):  
Yong Chang Kim ◽  
Toshiyuki Sugawa
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Uniformly Locally Univalent

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

scholarly journals ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS

2007 ◽  
Vol 49 (1) ◽  
pp. 45-52 ◽  
Author(s):  
STEPHAN RUSCHEWEYH ◽  
LUIS SALINAS
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Boundary Point ◽  
Univalent Functions ◽  
Gegenbauer Polynomials ◽  
Gauss Hypergeometric Function ◽  
Coefficient Estimates ◽  
Image Position

Abstract.D. Brannan's conjecture says that for 0 <α,β≤1, |x|=1, and n∈N one has |A2n−1(α,β,x)|≤|A2n−1(α,β,1)|, where We prove this for the case α=β, and also prove a differentiated version of the Brannan conjecture. This has applications to estimates for Gegenbauer polynomials and also to coefficient estimates for univalent functions in the unit disk that are ‘starlike with respect to a boundary point’. The latter application has previously been conjectured by H. Silverman and E. Silvia. The proofs make use of various properties of the Gauss hypergeometric function.

scholarly journals Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem
Keyword(s):  
Linear Combination ◽  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Faber Polynomials ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class

In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.

scholarly journals Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

We introduce and investigate a new general subclass ℋΣλ,μ(φ;Θ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

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.

Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

2018 ◽  
Vol 68 (2) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmad Zireh ◽  
Ebrahim Analouei Adegani ◽  
Mahmood Bidkham
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Polynomial Coefficient ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Faber Polynomial

Abstract In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes $\begin{array}{} H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h) \end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

scholarly journals Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

2021 ◽  
Vol 39 (2) ◽  
pp. 87-104
Author(s):  
Ebrahim Analouei Adegani ◽  
Ahmad Zireh ◽  
Mostafa Jafari
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In this work, we introduce a new subclas of bi-univalent functions which is defined by Hadamard product andsubordination in the open unit disk. and find upper bounds for the second and third coefficients for functions in this new subclass. Further, we generalize and improve some of the previously published results.

scholarly journals Coefficient estimates for certain subclasses of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (2) ◽  
pp. 351-360 ◽  
Author(s):  
Yong Sun ◽  
Yue-Ping Jiang ◽  
Antti Rasila
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

For ? ? 0 and 0 ? ? < 1 < ?, we denote by K(?,?,?) the class of normalized analytic functions satisfying the two sided-inequality ? < K (Zf'(z)/f(z) + z2f''(z)/f(z))<? (z ? U), where U is the open unit disk. Let K? (?, ?, ?) be the class of bi-univalent functions such that f and its inverse f-1 both belong to the class K(?, ?, ?). In this paper, we establish bounds for the coefficients, and solve the Fekete-Szeg? problem, for the class K((?,?,?). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coefficients of the functions in the class K? (?,?,?)

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