Techniques of the differential subordination for domains bounded by conic sections
We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp′(z))∈D⇒p(z)≺q(z), where D and q(𝒰) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q(𝒰). Also, we find the best do...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203302212 |
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| Summary: | We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp′(z))∈D⇒p(z)≺q(z), where D and q(𝒰) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q(𝒰). Also, we find the best dominant of the differential subordination p(z)+(zp′(z)/(βp(z)+γ))≺pk(z), when the function pk(k∈[0,∞)) maps the unit disk onto a conical domain contained in a right half-plane. Various applications in the theory of univalent functions are also given. |
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| ISSN: | 0161-1712 1687-0425 |