Coefficient Conditions for Starlikeness of Nonnegative Order
Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z)= E°°k=1 akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2012
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| Subjects: | |
| Online Access: | http://eprints.usm.my/38458/1/Coefficient_Conditions_for_Starlikeness_of_Nonnegative_Order.pdf http://eprints.usm.my/38458/ https://doi.org/10.1155/2012/450318 |
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| Summary: | Sufficient conditions on a sequence {ak} of nonnegative numbers are obtained that ensures f(z)= E°°k=1 akzk is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric
sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction
of the imaginary axis are also established. These results are applied to investigate the starlikeness
of functions involving the Gaussian hypergeometric functions. |
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