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https://ptsldigital.ukm.my/jspui/handle/123456789/499435| Title: | Certain problems on generalized derivative operators and the other class of analytic functions |
| Authors: | Ma'moun Ibraheem Ya'qoup Harayzeh (P46208) |
| Supervisor: | Maslina Darus, Prof. Dr. |
| Keywords: | Problems Generalized derivative operators Analytic functions Operator theory |
| Issue Date: | 20-Dec-2011 |
| Description: | The main objective of this thesis is to study certain problems on generalized derivative operators and the other class of functions which are analytic in the unit disk and normalized by the conditions and . In the beginning of this thesis, a selection of some main definitions together with a few of known theorems, which are required for the results in the subsequent chapters of this thesis, will be given. Indeed, a simple idea about some basic concepts in the theory of analytic functions and the theory of univalent functions will be mentioned. A new generalized derivative operator is introduced. This operator generalized many well-known operators studied earlier by many different authors. Using certain equalities relation some of the properties of differential subordination are posed and studied. Several interesting properties of inclusion and other applications of the new generalized derivative operator are investigated. New classes of analytic functions containing the generalized Ruscheweyh derivative operator which are defined by means of the Hadamard product and subordination will be introduced. Various inclusion properties of these classes are investigated. In addition inclusion relationships between these new classes and other known classes are determined. Some integral preserving properties are also considered. Next, by making use of the new generalized derivative operator, certain classes of analytic functions defined in the open unit disk, defined by means of the Hadamard product (or convolution) and subordination will also be introduced. Moreover, several inclusion properties of these classes are posed and investigated. Fekete-Szegö problems for functions belonging to the class defined by generalized derivative operator and the other class of analytic functions are studied. Hankel determinant for the class of analytic functions defined by generalized derivative operator are illustrated and discussed. The normal properties such as coefficient inequalities, growth and distortion theorems, extreme points, radius of starlikeness and convexity for the classes of analytic functions defined by generalized derivative operator are posed and studied. Finally, several interesting subordination results involving the Hadamard product (or convolution) are discussed for the same classes aforementioned. Various corollaries and consequences of the main subordination results of the earlier studies are also constructed and discussed. Interestingly we discovered that the results reduced to the class of starlike function of order and the class of convex function of order respectively, from various classes.,Ph.D |
| Pages: | 144 |
| Call Number: | QA329.H346 2011 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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