Generalized Alpha-Close-to-Convex Functions
We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ) if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; α∈[0,1]; β∈(−π/2,π/2), where ϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other pr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/830592 |
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| Summary: | We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ)
if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; α∈[0,1]; β∈(−π/2,π/2),
where ϕ
is a function of bounded boundary rotation. Coefficient estimates, an inclusion
result, arclength problem, and some other properties of these classes are studied. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |