Subordination by convex functions
For a fixed analytic function g(z)=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ) denote the class of all analytic functions f(z)=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ), a subordination result is derived involving the convolution with a normalized convex fun...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/62548 |
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| _version_ | 1832560172077154304 |
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| author | Rosihan M. Ali V. Ravichandran N. Seenivasagan |
| author_facet | Rosihan M. Ali V. Ravichandran N. Seenivasagan |
| author_sort | Rosihan M. Ali |
| collection | DOAJ |
| description | For a fixed analytic function g(z)=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ) denote the class of all analytic functions f(z)=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works. |
| format | Article |
| id | doaj-art-36ef60a695114462a89c16faeebdc8a9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-36ef60a695114462a89c16faeebdc8a92025-02-03T01:28:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/6254862548Subordination by convex functionsRosihan M. Ali0V. Ravichandran1N. Seenivasagan2School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, MalaysiaFor a fixed analytic function g(z)=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ) denote the class of all analytic functions f(z)=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.http://dx.doi.org/10.1155/IJMMS/2006/62548 |
| spellingShingle | Rosihan M. Ali V. Ravichandran N. Seenivasagan Subordination by convex functions International Journal of Mathematics and Mathematical Sciences |
| title | Subordination by convex functions |
| title_full | Subordination by convex functions |
| title_fullStr | Subordination by convex functions |
| title_full_unstemmed | Subordination by convex functions |
| title_short | Subordination by convex functions |
| title_sort | subordination by convex functions |
| url | http://dx.doi.org/10.1155/IJMMS/2006/62548 |
| work_keys_str_mv | AT rosihanmali subordinationbyconvexfunctions AT vravichandran subordinationbyconvexfunctions AT nseenivasagan subordinationbyconvexfunctions |