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 Radius of univalence and starlikeness of a class of analytic functions

1972 ◽  
Vol 14 (1) ◽  
pp. 1-8
Author(s):  
R. S. Gupta
Keyword(s):  
Analytic Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
The Family ◽  
Image Position ◽  
Class Of Functions ◽  
Radius Of Univalence

Letp denote the family of functions regular in E{z:|z| < 1} and with positive real part there. We propose to study, in this article, the subclass p2a1 of p whose functions P(z) have pre-assigned second coefficient 2a1. In what follows we may assume, without loss in generality, that a1 is real and non-negative. This assumption will be made throughout. As is well known [2], 0 ≦ a1 ≦ 1. In Theorem 1 we derive a generalization of Zmorovic's theorem 1, [3]. determine the radius of univalence and starlikeness of the class of functions

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