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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 459-483
http://dx.doi.org/10.1155/S0161171282000441

Univalence of normalized solutions of W(z)+p(z)W(z)=0

Department of Mathematical Sciences, Kent State University, Kent 44242, Ohio, USA

Received 27 August 1981

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Denote solutions of W(z)+p(z)W(z)=0 by Wα(z)=zα[1+n=1anzn] and Wβ(z)=zβ[1+n=1bnzn], where 0<(β)1/2(α) and z2p(z) is holomorphic in |z|<1. We determine sufficient conditions on p(z) so that [Wα(z)]1/α and [Wβ(z)]1/β are univalent in |z|<1.