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

R. K. Brown

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-25

Abstract:

Denote solutions of W ″ ( z ) + p ( z ) W ( z ) = 0 by W α ( z ) = z α [ 1 + ∑ n = 1 ∞ a n z n ] and W β ( z ) = z β [ 1 + ∑ n = 1 ∞ b n z n ] , where 0 < ℛ ( β ) ≤ 1 / 2 ≤ ℛ ( α ) and z 2 p ( z ) is holomorphic in | z | < 1 . We determine sufficient conditions on p ( z ) so that [ W α ( z ) ] 1 / α and [ W β ( z ) ] 1 / β are univalent in | z | < 1 .

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:864349

DOI: 10.1155/S0161171282000441

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