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

R. K. Brown
1982 International Journal of Mathematics and Mathematical Sciences  
Denote solutions ofW″(z)+p(z)W(z)=0byWα(z)=zα[1+∑n=1∞anzn]andWβ(z)=zβ[1+∑n=1∞bnzn], where0<ℛ(β)≤1/2≤ℛ(α)andz2p(z)is holomorphic in|z|<1. We determine sufficient conditions onp(z)so that[Wα(z)]1/αand[Wβ(z)]1/βare univalent in|z|<1.
doi:10.1155/s0161171282000441 fatcat:3krhyvai5zdvloqoajofoyol24