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Abstract
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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

R.K. Brown

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

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.