Subordination criteria for starlikeness and convexity
For functions p analytic in the open unit disc U={z:|z|<1} with the normalization p(0)=1, we consider the families 𝒫[A,−1], −1<A≤1, consisting of p such that p(z) is subordinate to (1+Az)/(1−z) in U and 𝒫(1,b), b>0, consisting of p, which have the disc formulation |p−1|<b in U. We then i...
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| Main Authors: | , |
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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/S0161171203207146 |
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| Summary: | For functions p analytic in the open unit disc U={z:|z|<1} with the normalization p(0)=1, we consider the families 𝒫[A,−1], −1<A≤1, consisting of p such that p(z) is subordinate to (1+Az)/(1−z) in U and 𝒫(1,b), b>0,
consisting of p, which have the disc formulation |p−1|<b in U. We then introduce subordination criteria for the choice of
p(z)=zf′(z)/f(z), where f is analytic in U and normalized by f(0)=f′(0)−1=0. We also obtain starlikeness and convexity
conditions for such functions f and consequently extend and, in
some cases, improve the corresponding previously known results. |
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| ISSN: | 0161-1712 1687-0425 |