Certain sufficient conditions for univalence

Certain sufficient conditions for univalence 1

In this paper, we determined conditions on β, αi and fi(z) so that the integral operator { β ∫ z 0 tβ−1 n ∏ i=1 ( fi(t) t ) 1 αi dt } 1 β is univalent in the open unit disk for the two subclasses analytic functions. 2000 Mathematical Subject Classification: Primary 30C80, Secondary 30C45.

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

Some Sufficient Conditions for Univalence

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

SUFFICIENT CONDITIONS FOR UNIVALENCE IN Cn

On Some Sufficient Conditions for Univalence

In this paper the method of subordination chains is used to establish some sufficient conditions for univalence for analytic functions defined in the open unit disk.