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https://ptsldigital.ukm.my/jspui/handle/123456789/499492| Title: | Some Selected Topics Related To Subclasses Of Analytic Functions |
| Authors: | Nagat M. Mustafa Muftah (P50029) |
| Supervisor: | Maslina Darus, Prof. Dr. |
| Keywords: | Selected Topics Related To Subclasses Of Analytic Functions Subclasses Of Analytic Functions Analytic Functions Analytic functions |
| Issue Date: | 13-Jun-2013 |
| Description: | The main objective of this thesis is to study some properties for certain subclasses of normalised analytic and normalised multivalent analytic functions in the unit disc. Some basic definitions and initial results of geometric function theory that will be used in the subsequent chapters are summarised. First of all, new integral operator is defined on the class of normalised analytic functions. This operator is associated to Hurwitz-Lerch zeta function and is known as the generalised integral operator. With this generalised integral operator, a subclass of analytic function is introduced. Some properties such as the coefficient bounds, distortion bounds, extreme points, integral means, Hadamard product, radii of close-to-convexity, starlikeness, convexity and partial sums are given. Next, the generalised derivative operator defined on the class of normalised analytic function is given. New subclass of analytic functions is also introduced here. Sharp bounds for the nonlinear functional are obtained. Then, sharp upper bounds for the Fekete-Szego functional are obtained and new special cases of the results are pointed out. Furthermore, the coefficient bounds, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass with negative coefficients are also obtained. By using the same generalised derivative operator, a new family of integral operator is introduced and their univalence properties are studied. Further, the generalised derivative operator defined on the class of multivalent functions is given and new subclasses are introduced. In addition, another new subclasses are introduced and several inclusion relations are given. Some results given by subordinations techniques are also studied for the aforementioned generalised derivative operator of multivalent function. Finally, two new integral operators and two subclasses of p-valent functions are introduced and some properties are obtained.,PhD |
| Pages: | 131 |
| Call Number: | QA331 .M836 2013 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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