Integral means of certain class of analytic functions
In this paper we discuss the following class of functions Sλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1, and f(z)=z+∑n=2∞anzn is analytic in D={z:|z|<1}, g(z) is a starlike function of order α. A subordination about this class is obtained, the integral means of...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000572 |
| Summary: | In this paper we discuss the following class of functions
Sλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D} where 0≤λ≤1,0<β≤1,0≤α<1,
and f(z)=z+∑n=2∞anzn is analytic in D={z:|z|<1}, g(z) is a starlike function of order α. A
subordination about this class is obtained, the integral means of functions in Sλ(α,β) and some
extremal properties are studied. |
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| ISSN: | 0161-1712 1687-0425 |