On univalent functions, Bloch functions and VMOA

1978 ◽  
Vol 236 (3) ◽  
pp. 199-208 ◽  
Author(s):  
Ch. Pommerenke
Keyword(s):  
Univalent Functions ◽  
Bloch Functions

scholarly journals The boundary behavior of Bloch functions and univalent functions.

1988 ◽  
Vol 35 (2) ◽  
pp. 313-320 ◽  
Author(s):  
J. M. Anderson ◽  
L. D. Pitt
Keyword(s):  
Boundary Behavior ◽  
Univalent Functions ◽  
Bloch Functions

scholarly journals Univalent Functions in the Möbius InvariantQKSpace

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Fernando Pérez-González ◽  
Jouni Rättyä
Keyword(s):  
Univalent Function ◽  
Univalent Functions ◽  
Regularity Conditions ◽  
Bloch Functions

It is shown that a univalent functionfbelongs toQKif and only ifsup a∈𝔻∫01M∞2(r,f∘φa-f(a))K′(log (1/r))dr<∞, whereφa(z)=(a-z)/(1-a¯z), providedKsatisfies certain regularity conditions. It is also shown that under these conditionsQKcontains all univalent Bloch functions if and only if∫01(log ((1+r)/(1-r)))2K′(log (1/r))dr<∞.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

Radius problems for univalent functions

2020 ◽  
Vol 26 (1) ◽  
pp. 111-115
Author(s):  
Janusz Sokół ◽  
Katarzyna Trabka-Wiȩcław
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Radius Problems ◽  
Radius Of Convexity

AbstractThis paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

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