International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 459-483
doi: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 R. K. Brown. 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=1∞anzn] and Wβ(z)=zβ[1+∑n=1∞bnzn], where 0<ℛ(β)≤1/2≤ℛ(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.