Starlikeness of Analytic Functions with Subordinate Ratios
Let h be a nonvanishing analytic function in the open unit disc with h0=1. Consider the class consisting of normalized analytic functions f whose ratios fz/gz, gz/zpz, and pz are each subordinate to h for some analytic functions g and p. The radius of starlikeness of order α is obtained for this cla...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
Hindawi Limited
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/17ab32d09f1340769955c87e711c6e96 |
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| Summary: | Let h be a nonvanishing analytic function in the open unit disc with h0=1. Consider the class consisting of normalized analytic functions f whose ratios fz/gz, gz/zpz, and pz are each subordinate to h for some analytic functions g and p. The radius of starlikeness of order α is obtained for this class when h is chosen to be either hz=1+z or hz=ez. Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness. |
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