An extension of Becker's univalence condition

1976 ◽  
Vol 220 (3) ◽  
pp. 285-290 ◽  
Author(s):  
Stephan Ruscheweyh
Keyword(s):  
Univalence Condition

On an extension of Ozaki’s condition

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Convex Domain ◽  
Univalence Condition ◽  
Radius Of Univalence

Abstract It is known that if {f(z)=z^{p}+\sum_{n=p+1}^{\infty}a_{n}z^{n}} and it is analytic in a convex domain {D\subset\mathbb{C}} and, for some real α, we have {\operatorname{\mathfrak{Re}}\{\exp(i\alpha)f^{(p)}(z)\}>0} , {z\in D} , then {f(z)} is at most p-valent in D. This Ozaki condition is a generalization of the well-known Noshiro–Warschawski univalence condition. In this paper, we consider the radius of univalence of functions {g(z)=z+\sum_{n=1}^{\infty}b_{n}z^{n}} such that {g^{\prime}(z)\prec[(1+z)^{2}/(1-z)^{2}]} and some related problems.

Univalence Condition for an Integral Operator

2013 ◽  
Vol 4 (1) ◽  
pp. 8-10
Author(s):  
Nicoleta Ularu
Keyword(s):  
Integral Operator ◽  
Univalence Condition

scholarly journals Univalency and Convexity Conditions for a General Integral Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Serap Bulut ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Univalence Condition ◽  
General Integral ◽  
Order Of Convexity ◽  
General Integral Operator ◽  
Convexity Conditions

For analytic functions f and g in the open unit disc 𝕌, a new general integral operator is introduced. The main objective of this paper is to obtain univalence condition and order of convexity for this general integral operator.

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