scholarly journals A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

2008 ◽  
Vol 156 (2) ◽  
pp. 167-173 ◽  
Author(s):  
Toshiyuki Sugawa ◽  
Takao Terada
Keyword(s):  
Univalent Functions ◽  
Bloch Functions ◽  
Coefficient Inequality ◽  
Uniformly Locally Univalent

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 Certain Subclass of Univalent Functions Involving Fractional Q-Calculus Operator

2017 ◽  
Vol 13 (4) ◽  
pp. 7370-7378
Author(s):  
Mustafa Ibrahim HAMEED
Keyword(s):  
Integral Operator ◽  
Univalent Function ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Geometric Properties ◽  
Coefficient Inequality ◽  
Operator Mean

The main object of the present paper is to introduce certain subclass of univalent function associated with the concept of differential subordination. We studied some geometric properties like coefficient inequality and nieghbourhood property, the Hadamard product properties and integral operator mean inequality.

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<∞.

On univalent functions, Bloch functions and VMOA

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