A note on Bazilevič functions
For α>0, let B1(α) be the class of normalized analytic functions defined in the open unit disc D satisfying Re(f(z)/z)α−1f′(z)>0 for z∈D. The sharp lower bound for Re(f(z)/z)α is obtained and the result is generalized to some iterated integral operators.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291001126 |
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| _version_ | 1832551666373623808 |
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| author | S. A. Halim D. K. Thomas |
| author_facet | S. A. Halim D. K. Thomas |
| author_sort | S. A. Halim |
| collection | DOAJ |
| description | For α>0, let B1(α) be the class of normalized analytic functions defined in the open
unit disc D satisfying Re(f(z)/z)α−1f′(z)>0 for z∈D. The sharp lower bound for Re(f(z)/z)α is
obtained and the result is generalized to some iterated integral operators. |
| format | Article |
| id | doaj-art-48e58b2918ae4e24bba1f79f5cacc2bf |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-48e58b2918ae4e24bba1f79f5cacc2bf2025-02-03T06:00:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114482182310.1155/S0161171291001126A note on Bazilevič functionsS. A. Halim0D. K. Thomas1Department of Mathematics and Computer Science, University of Swansea, Singleton Park, Swansea SA2 8PP, UKDepartment of Mathematics and Computer Science, University of Swansea, Singleton Park, Swansea SA2 8PP, UKFor α>0, let B1(α) be the class of normalized analytic functions defined in the open unit disc D satisfying Re(f(z)/z)α−1f′(z)>0 for z∈D. The sharp lower bound for Re(f(z)/z)α is obtained and the result is generalized to some iterated integral operators.http://dx.doi.org/10.1155/S0161171291001126Bazilevič functions and integral operators. |
| spellingShingle | S. A. Halim D. K. Thomas A note on Bazilevič functions International Journal of Mathematics and Mathematical Sciences Bazilevič functions and integral operators. |
| title | A note on Bazilevič functions |
| title_full | A note on Bazilevič functions |
| title_fullStr | A note on Bazilevič functions |
| title_full_unstemmed | A note on Bazilevič functions |
| title_short | A note on Bazilevič functions |
| title_sort | note on bazilevic functions |
| topic | Bazilevič functions and integral operators. |
| url | http://dx.doi.org/10.1155/S0161171291001126 |
| work_keys_str_mv | AT sahalim anoteonbazilevicfunctions AT dkthomas anoteonbazilevicfunctions AT sahalim noteonbazilevicfunctions AT dkthomas noteonbazilevicfunctions |