Sufficient conditions for starlikeness associated with parabolic region
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 Rew>|w−1|. This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007895 |
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| Summary: | 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 Rew>|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+αf′(z)(f(z)/z) μ−1≺1+λz, is in S p. |
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| ISSN: | 0161-1712 1687-0425 |