Omar, Rashidah (2012) *Properties of Analytic and Harmonic Functions / Rashida binti Omar.* PhD thesis, University of Malaya.

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## Abstract

The starlikeness of integral transform V_f(z) = R 1 0 _(t) f(tz) t dt was _rst studied by Fournier and Ruscheweyh in 1994. This investigation is extended to starlikeness and convexity of order _ where _ 2 (0; 1 2 ]. Making use the class introduced by Rosihan et al. (2012b), we determine the starlikeness and convexity of order _ for the integral transforms V_f using the concept of duality and Herglotz formula. In addition, a su_cient condition for V_f to be starlike and convex functions order _ and some applications of certain operators are also looked at. Furthermore, these properties are obtained for the integral transform V_f(z) = z R 1 0 _(t) 1

Item Type: | Thesis (PhD) |
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Additional Information: | Ph.D Institut Sains Matematik, Fakulti Sains, Universiti Malaya 2013 |

Uncontrolled Keywords: | Analytic functions; Harmonic functions; Functions of complex variables |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Divisions: | Faculty of Science |

Depositing User: | Miss Dashini Harikrishnan |

Date Deposited: | 26 Sep 2014 12:07 |

Last Modified: | 26 Sep 2014 12:07 |

URI: | http://studentsrepo.um.edu.my/id/eprint/4238 |

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