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https://ptsldigital.ukm.my/jspui/handle/123456789/500456| Title: | On certain differential and integral operators in geometric function theory |
| Authors: | Muhammad Imran Faisal (P46743) |
| Keywords: | Universiti Kebangsaan Malaysia -- Dissertations Geometric function theory Functions of complex variables |
| Issue Date: | 15-Sep-2012 |
| Description: | In this thesis, all four major classes of functions in Geometric Function Theory have been studied namely, the class of univalent functions, p-valent analytic functions, meromorphic functions and p-valent meromorphic functions. For class of analytic functions, we introduce a family of integral operators. By using integral operator, we introduce new criteria to prove that the analytic function is univalent. Such criteria extended the earlier criteria introduced by Becker in 1973 and Ahlfor in 1974. In addition, we also introduce a differential operator for analytic functions of complex order. For analytic functions of complex order, we introduce certain new subclasses and discuss their several properties such as neighborhood properties, coefficient estimates, Hadamard product, extreme points, integral mean inequalities and inclusion properties. Later, using the operator defined in the class of multivalent functions we introduce certain subclasses of p-valent functions and discuss its inclusion and integral-preserving properties. We introduce a special family of p-valent functions and discuss its inclusion and sufficient conditions. We also introduce certain subclasses of meromorphic and p-valent meromorphic functions by using the differential operators that we have introduced in their respective spaces. Furthermore, for such subclasses of meromorphic and p-valent meromorphic functions we again discuss its inclusion and integral properties. Finally, we discuss subordination properties, superordination properties and sandwich results for the functions belonging to the subclasses of analytic and multivalent functions.,Certification of Masters/ Doctorial Thesis" is not available |
| Pages: | 122 |
| Call Number: | QA360.M838 2012 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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