Please use this identifier to cite or link to this item:
https://ptsldigital.ukm.my/jspui/handle/123456789/499987| Title: | A study on classes of complex functions defined by new differential operators |
| Authors: | Mohammad Zakariya Salameh Al-Kaseasbeh (P72630) |
| Supervisor: | Maslina Darus, Prof. Dr. |
| Keywords: | Functions Operators Classes Differential operator |
| Issue Date: | 1-Nov-2017 |
| Description: | This thesis deals with problems related to new differential operators. The idea is motivated from the operators introduced by Ruscheweyh in 1970's and by Sˇalˇagean in 1980's. Extension from both operators, variety of generalised differential operators are introduced and seen in various medium of publications. In this study, two differential operators of complex function are constructed by means of linear combination and convolution. Later, those two constructed differential operators are utilised to define classes of geometric functions which take the form of analytic, meromorphic and harmonic functions. By doing so, new classes of geometric functions based on analytic, meromorphic and harmonic functions are introduced. For each of these classes, several properties are investigated. These include the coefficient bounds, distortion theorem, extreme points and convolution properties. Adding to that, other properties such as the Fekete-Szego problem and inclusion relations are also given for certain classes of analytic functions, whereas the radii of convexity and starlikeness together with partial sums are studied for the classes of meromorphic functions. One of these properties is generalised using Hadamard-Holder products. Also, in this study, two classes of uniformly geometric functions involving the constructed differential operators are defined. Moreover, a geometric interpretation of such functions is also presented. In fact, the coefficient bounds and inclusion relations are obtained. Subordination and superordination conditions that involved constructed differential operators are investigated as well. This leads to the sandwich-type results. Finally, concave meromorphic functions are studied and their properties are given. These concave meromorphic functions are then defined by the operators and their properties are obtained.,Certification of Master's/Doctoral Thesis" is not available |
| Pages: | 128 |
| Call Number: | QA329.4.K337 2017 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_97558+SOURCE1+SOURCE1.0.PDF Restricted Access | 248.78 kB | Adobe PDF |  View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.