On Sakaguchi functions
Let Ss(α)(0≤α<1/2) be the class of functions f(z)=z+⋯ which are analytic in the unit disk and satisfy there Re{zf′(z)/(f(z)−f(−z))}>α. In the present paper, we find the sharp lower bound on Re{(f(z)−f(−z))/z} and investigate two subclasses S0(α) and T0(α) of Ss(α). We derive sharp distortion i...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203205330 |
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| _version_ | 1832562933734834176 |
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| author | Ding-Gong Yang Jin-Lin Liu |
| author_facet | Ding-Gong Yang Jin-Lin Liu |
| author_sort | Ding-Gong Yang |
| collection | DOAJ |
| description | Let Ss(α)(0≤α<1/2) be the class of functions
f(z)=z+⋯ which are analytic in the unit disk and satisfy
there Re{zf′(z)/(f(z)−f(−z))}>α. In the present paper, we find the sharp lower bound on Re{(f(z)−f(−z))/z} and investigate two subclasses S0(α) and T0(α) of Ss(α). We derive sharp distortion inequalities and some
properties of the partial sums for functions in the classes
S0(α) and T0(α). |
| format | Article |
| id | doaj-art-2ec931e1cc6645588d31e3777ce7d79c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2ec931e1cc6645588d31e3777ce7d79c2025-02-03T01:21:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003301923193110.1155/S0161171203205330On Sakaguchi functionsDing-Gong Yang0Jin-Lin Liu1Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, ChinaDepartment of Mathematics, Yangzhou University, Yangzhou, Jiangsu 225002, ChinaLet Ss(α)(0≤α<1/2) be the class of functions f(z)=z+⋯ which are analytic in the unit disk and satisfy there Re{zf′(z)/(f(z)−f(−z))}>α. In the present paper, we find the sharp lower bound on Re{(f(z)−f(−z))/z} and investigate two subclasses S0(α) and T0(α) of Ss(α). We derive sharp distortion inequalities and some properties of the partial sums for functions in the classes S0(α) and T0(α).http://dx.doi.org/10.1155/S0161171203205330 |
| spellingShingle | Ding-Gong Yang Jin-Lin Liu On Sakaguchi functions International Journal of Mathematics and Mathematical Sciences |
| title | On Sakaguchi functions |
| title_full | On Sakaguchi functions |
| title_fullStr | On Sakaguchi functions |
| title_full_unstemmed | On Sakaguchi functions |
| title_short | On Sakaguchi functions |
| title_sort | on sakaguchi functions |
| url | http://dx.doi.org/10.1155/S0161171203205330 |
| work_keys_str_mv | AT dinggongyang onsakaguchifunctions AT jinlinliu onsakaguchifunctions |