scholarly journals Radius of univalence of certain class of analytic functions

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 1085-1090 ◽  
Author(s):  
M. Obradovic ◽  
S. Ponnusamy
Keyword(s):  
Analytic Functions ◽  
Radius Of Univalence

scholarly journals Radius Constants for Functions with the Prescribed Coefficient Bounds

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Om P. Ahuja ◽  
Sumit Nagpal ◽  
V. Ravichandran
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Harmonic Mappings ◽  
Coefficient Bounds ◽  
Coefficient Inequality ◽  
Coefficient Bound ◽  
Radius Of Univalence

For an analytic univalent functionf(z)=z+∑n=2∞anznin the unit disk, it is well-known thatan≤nforn≥2. But the inequalityan≤ndoes not imply the univalence off. This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of orderα  (0≤α<1) for functions with prescribed coefficient bound on the analytic part.

scholarly journals On the radius of univalence of convex combinations of analytic functions

1983 ◽  
Vol 6 (2) ◽  
pp. 335-340
Author(s):  
Khalida I. Noor ◽  
Fatima M. Aloboudi ◽  
Naeela Aldihan
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Radius Of Univalence

We consider forα>0, the convex combinationsf(z)=(1−α)F(z)+αzF′(z), whereFbelongs to different subclasses of univalent functions and find the radius for whichfis in the same class.

scholarly journals The radius of univalence of certain analytic functions

1976 ◽  
Vol 32 (2) ◽  
pp. 119-128
Author(s):  
P. L. Bajpai ◽  
Prem Singh
Keyword(s):  
Analytic Functions ◽  
Radius Of Univalence
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