×

Certain sufficient conditions for univalence. (English) Zbl 1199.30161

Summary: We determine conditions on \(\beta \), \(\alpha _i\) and \(f_i(z)\) so that the integral operator \(\left\{ {\beta \int_0^z t^{\beta -1} \prod_{i=1}^n (\frac{f_i(t)}t)^{\frac1{\alpha _i}}dt}\right\} ^\frac1{\beta}\) is univalent in the open unit disk for the two subclasses analytic functions.

MSC:

30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDFBibTeX XMLCite
Full Text: EuDML