Let f z szqΓ a z be the sequence of partial sums of a function a z that is analytic in z -1 and either starlike of order β£ or ks 2 k Γ 4 convex of order β£, 0 F β£ -1. When the coefficients a are ''small,'' we deterk Γ Ε½ . Ε½ 4 Γ Ε½ . Ε½ .4 Γ Ε½ . X Ε½ .4 mine lower bounds on Re f z rf z , Re f z rf z , R
Starlike and Convexity Properties for Hypergeometric Functions
β Scribed by H. Silverman
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 195 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
## Abstract The object of the present paper is to prove some interesting sufficient conditions for __p__βvalently closeβtoβconvex and starlike functions in the unit disk.
Let z be an analytic function with positive real part on β¬ s z; z -1 with Ε½ . Ε½ . 0 s 1, Π 0 ) 0 which maps the unit disk β¬ onto a region starlike with respect Ε½ . to 1 and symmetric with respect to the real axis. Let ST denote the class of Ε½ . Ε½ . Ε½ . Ε½ . Ε½ . Ε½ . analytic functions f z with f 0 s
In this paper the classes of uniformly convex and uniformly starlike functions are Ε½ presented as dual sets for certain function families in the sense of convolution . theory . The results are used to find some sharp sufficient conditions for functions, regular in the unit disk, to belong to the abo