ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXVI, 2 (2007)
p. 137 - 142
An Integral Univalent Operator
D. Breaz and N. Breaz

Abstract.  In this paper we consider the class of univalent functions defined by the condition |(z2f '(z))/(f 2(z))- 1| <1, z Î U, where f(z) = z + a2z2 + ¼ is an analytic function in the unit disc
U = {z Î C : |z| < 1}. We present univalence conditions for the operator
Ga, n(z) = ( (n(a -1) + 1)
z
ò
0
g1a - 1 (t) ¼ gna - 1(t) dt ) 1/(n(a -1) + 1).


Keywords: univalent operator, unit disc, univalent functions.  

AMS Subject classification. Primary: 30C45.
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