A Third-Order Differential Equation and Starlikeness of a Double Integral Operator
Functions f(z)=z+∑2∞anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operat...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/901235 |
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| author | Rosihan M. Ali See Keong Lee K. G. Subramanian A. Swaminathan |
| author_facet | Rosihan M. Ali See Keong Lee K. G. Subramanian A. Swaminathan |
| author_sort | Rosihan M. Ali |
| collection | DOAJ |
| description | Functions f(z)=z+∑2∞anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z)=∫01∫01G(ztμsν)t-μs-νds dt with G' subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h. |
| format | Article |
| id | doaj-art-9f179b8a0ac048e9baecb9879fd8ca59 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9f179b8a0ac048e9baecb9879fd8ca592025-02-03T01:27:30ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/901235901235A Third-Order Differential Equation and Starlikeness of a Double Integral OperatorRosihan M. Ali0See Keong Lee1K. G. Subramanian2A. Swaminathan3School 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, MalaysiaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, IndiaFunctions f(z)=z+∑2∞anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(z)=g(z) are considered, where g is subordinated to a normalized convex univalent function h. These functions f are given by a double integral operator of the form f(z)=∫01∫01G(ztμsν)t-μs-νds dt with G' subordinated to h. The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h.http://dx.doi.org/10.1155/2011/901235 |
| spellingShingle | Rosihan M. Ali See Keong Lee K. G. Subramanian A. Swaminathan A Third-Order Differential Equation and Starlikeness of a Double Integral Operator Abstract and Applied Analysis |
| title | A Third-Order Differential Equation and Starlikeness of a Double Integral Operator |
| title_full | A Third-Order Differential Equation and Starlikeness of a Double Integral Operator |
| title_fullStr | A Third-Order Differential Equation and Starlikeness of a Double Integral Operator |
| title_full_unstemmed | A Third-Order Differential Equation and Starlikeness of a Double Integral Operator |
| title_short | A Third-Order Differential Equation and Starlikeness of a Double Integral Operator |
| title_sort | third order differential equation and starlikeness of a double integral operator |
| url | http://dx.doi.org/10.1155/2011/901235 |
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