On univalent functions defined by a generalized Sălăgean operator
We introduce a class of univalent functions Rn(λ,α) defined by a new differential operator Dnf(z), n∈ℕ0={0,1,2,…}, where D0f(z)=f(z), D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z), λ≥0, and Dnf(z)=Dλ(Dn−1f(z)). Inclusion relations, extreme points of Rn(λ,α), some convolution properties of functions belonging to R...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204108090 |
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| Summary: | We introduce a class of univalent functions
Rn(λ,α) defined by a new differential operator
Dnf(z), n∈ℕ0={0,1,2,…}, where
D0f(z)=f(z), D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z), λ≥0, and
Dnf(z)=Dλ(Dn−1f(z)). Inclusion relations,
extreme points of Rn(λ,α), some convolution
properties of functions belonging to Rn(λ,α), and
other results are given. |
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| ISSN: | 0161-1712 1687-0425 |