On certain univalence criteria

Some criteria for univalence of certain integral operators

We derive some criteria for univalence of certain integral operators for analytic functions in the open unit disk. 1. Introduction. Let Ꮽ be the class of the functions f (z) which are analytic in the open unit disk U = {z ∈ C : |z| < 1} and f (0) = f (0) − 1 = 0.

New Criteria for Univalence of Certain Integral Operators

Univalence of Certain Integral Operators

We study some integral operators and determine conditions for the univalence of these integral operators.

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.

Univalence criteria for general integral operator

Let A be the class of all analytic functions which are analytic in the open unit disc U = {z : |z| < 1} and Gb = { f ∈ A : ∣∣∣∣ 1 + zf ′′(z)/f ′(z) zf ′(z)/f(z) − 1 ∣∣∣∣ < b, z ∈ U } . In this paper, we derive sufficient conditions for the integral operator Ii γ (f1, ..., fn)(z) =    z ∫ 0 tγ−1 ( f ′ 1(t) )α1 ( f1(t) t )1−α1 ... ( f ′ n(t) )αn ( fn(t) t )1−αn dt    1 γ to be analytic and ...