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http://hdl.handle.net/2080/1119
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| DC Field | Value | Language |
|---|
| contributor.author | Bhowmik, B | - |
| contributor.author | Ponnusamy, S | - |
| contributor.author | Wirths, K J | - |
| date.accessioned | 2010-01-01T04:38:57Z | - |
| date.available | 2010-01-01T04:38:57Z | - |
| date.issued | 2009 | - |
| identifier.citation | Journal of Monatsh Math, (post print) | en |
| identifier.uri | http://dx.doi.org/10.1007/s00605-009-0146-7 | - |
| identifier.uri | http://hdl.handle.net/2080/1119 | - |
| description.abstract | Let Co(®) denote the class of concave univalent functions in the unit disk D. Each function f 2 Co(®) maps the unit disk D onto the complement of an unbounded convex set. In this paper we ¯nd the exact disk of variability for the functional (1¡jzj2) (f00(z)=f0(z)), f 2 Co(®). In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional (1 ¡ jzj2) (f00(z)=f0(z)),f 2 Co(®) whenever f00(0) is ¯xed. We also give a characterization for concave
functions in terms of Hadamard convolution. In addition to sharp coe±cient inequalities, we prove that functions in Co(®) belong to the Hp space for p < 1=®. | en |
| format.extent | 240173 bytes | - |
| format.mimetype | application/pdf | - |
| language.iso | en | - |
| publisher | Springer | en |
| title | Characterization and the Pre-Schwarzian Norm Estimate for Concave Univalent Functions | en |
| type | Article | en |
| Appears in Collections: | Journal Articles
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| bhowmik.pdf | | 234Kb | Adobe PDF | View/Open |
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