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https://ptsldigital.ukm.my/jspui/handle/123456789/500487| Title: | A study on certain operators and their properties |
| Authors: | Anessa Basher Ahmed Oshah (P72182) |
| Keywords: | Universiti Kebangsaan Malaysia -- Dissertations Operator theory Analytic functions Differential operators |
| Issue Date: | 31-Dec-2016 |
| Description: | This thesis deals with certain classes of analytic functions defined by certain operators. Some definitions and known results which are required in the subsequent studies are stated. A general idea on some subclasses of univalent functions, p-valent functions, Hadamard product, Fekete-Szego inequality and basic hypergeometric functions are presented. Another topic treated in this thesis is on basic theory of differential subordinations. To present our first results, a generalised differential operator is introduced and studied. Using the operator three subclasses of analytic functions are introduced and several inclusion relationships are obtained. For the same operator the generalised uniformly starlike and convex class of functions is given and coefficient inequalities are obtained. An upper bound of second Hankel determinant for a class of analytic functions is studied. Next, an operator associated with the generalised hypergeometric function of p-valent type is considered. By using the principle of differential subordination, some properties are investigated. A subclass of generalised hypergeometric p-valent functions of complex order is also introduced and majorisation properties are considered. After that, some subordination and superordination results involving are investigated. Some strong differential subordination and superordination implications involving the operator are studied which are acquired by taking into account suitableclasses of admissible functions. The sandwich-type theorems for the operators and _are also examined. Now, a new differential operator associated with Ruscheweyh operator and multiplier transformation is introduced. Here, several differential subordinations are obtained. Also, a new subclass of analytic functions with negative coefficients is given, and basic properties like coefficient inequalities,growth and distortion theorems are obtained. Next, new generalised integral operator is introduced and new subclasses of analytic functions of complex order are defined. For these classes, several Fekete-Szego problems are obtained. Another subclasses definedby a convolution between incomplete beta function and the generalised integral operator is given, and several interesting properties are obtained. Finally, the linear multiplier fractional differential operator is defined for the class of harmonic functions and several properties are studied,Tesis ini tiada Perakuan Tesis Sarjana / Doktor Falsafah" |
| Pages: | 149 |
| Call Number: | QA329.O838 2016 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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