Certain Conditions for Starlikeness of Analytic Functions of Koebe Type
For 𝛼≥0, 𝜆>0, we consider the 𝑀(𝛼,𝜆)𝑏 of normalized analytic 𝛼−𝜆 convex functions defined in the open unit disc 𝕌. In this paper, we investigate the class 𝑀(𝛼,𝜆)𝑏, that is, Re{(𝑧𝑓𝑏(𝑧)/𝑓𝑏(𝑧))[1−𝛼+𝛼(1−𝜆)(𝑧𝑓𝑏(𝑧)/𝑓𝑏(𝑧))+𝛼𝜆(1+(𝑧𝑓𝑏(𝑧)/𝑓𝑏(𝑧)))]}>0, with 𝑓𝑏 is Koebe type, that is, 𝑓𝑏(𝑧)∶=𝑧/(1−𝑧𝑛)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/679704 |