A class of bounded starlike functions
We consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000360 |
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| _version_ | 1850166566046400512 |
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| author | Herb Silverman |
| author_facet | Herb Silverman |
| author_sort | Herb Silverman |
| collection | DOAJ |
| description | We consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found. |
| format | Article |
| id | doaj-art-e3a826dce2b74ee08b49eacd7b66cbeb |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e3a826dce2b74ee08b49eacd7b66cbeb2025-08-20T02:21:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117224925210.1155/S0161171294000360A class of bounded starlike functionsHerb Silverman0Department of Mathematics, University of Charleston, Charleston 29424, SC, USAWe consider functions f(z)=z+… that are analytic in the unit disk and satisfy there the inequality Re(f′(z)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.http://dx.doi.org/10.1155/S0161171294000360univalentstarlike. |
| spellingShingle | Herb Silverman A class of bounded starlike functions International Journal of Mathematics and Mathematical Sciences univalent starlike. |
| title | A class of bounded starlike functions |
| title_full | A class of bounded starlike functions |
| title_fullStr | A class of bounded starlike functions |
| title_full_unstemmed | A class of bounded starlike functions |
| title_short | A class of bounded starlike functions |
| title_sort | class of bounded starlike functions |
| topic | univalent starlike. |
| url | http://dx.doi.org/10.1155/S0161171294000360 |
| work_keys_str_mv | AT herbsilverman aclassofboundedstarlikefunctions AT herbsilverman classofboundedstarlikefunctions |