Univalence of alexander transform under new mapping properties
Title:
Univalence of alexander transform under new mapping properties
Author:
Ponnusamy, S.
Appeared in:
Complex variables and elliptic equations
Paging:
Volume 30 (1996) nr. 1 pages 55-58
Year:
1996-05
Contents:
Let 2F1(a,b;c;z) and Φ(a;c;z) denote the Gaussian hypergeometric function and confluent hypergeometric function respectively. It is well known that if f is univalent in the unit disc δ then the corresponding Alexander transform of f, namely[image omitted] dt, is not necessarily univalent in the whole of δ In this paper we determine conditions on the parameters a,b and c so that the Alexander transform [image omitted] , where f(z)=z2F1(a,b;c;z) or zΦ(a;c;z) is univalent and starlike in the whole of δ. In particular, we obtain conditions on a,b,c to guarantee that 2F1(a,b;c;z) (and Φ(a;c;z) resp.) will be univalent in the whole of the unit disc.
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