Sufficient conditions for starlikeness associated with parabolic region

V. Ravichandran, A. Gangadharan and T. N. Shanmugam

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-6

Abstract:

An analytic function f ( z ) = z + a n + 1 z n + 1 + ⋯ , defined on the unit disk △ = { z : | z | < 1 } , is in the class S p if z f ′ ( z ) / f ( z ) is in the parabolic region Re w > | w − 1 | . This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in S p are obtained. In particular, we find condition on λ such that the function f ( z ) , satisfying ( 1 − α ) ( f ( z ) / z ) μ + α f ′ ( z ) ( f ( z ) / z ) μ − 1 ≺ 1 + λ z , is in S p .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:347928

DOI: 10.1155/S0161171202007895

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