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https://ptsldigital.ukm.my/jspui/handle/123456789/499711| Title: | Some contributions in linear operations for certain classes of analytic functions |
| Authors: | Abubaker Afaf A. Ali (P50037) |
| Supervisor: | Maslina Darus, Prof. Dr. |
| Keywords: | Linear operations Analytic functions Univalent functions Linear operators |
| Issue Date: | 1-Jan-2015 |
| Description: | Let S denote the class of analytic functions f which are univalent in the open unit discU = fz 2 C : jzj < 1g and normalized by the conditions f(0) = 0 and f0(0) = 1.The main objective of this thesis is to study some properties for subclasses of analytic univalent functions defined by linear operators. Some definitions and known results, which are required in subsequent chapters, are given in the first chapter. Indeed, a simple idea about the subclasses of univalent functions, growth and distortion theorems, Hadamard product, Hankel determinant, subordination and superordination principles, functions with positive real part, hypergeometric functions, harmonic functions, and some linear operators on analytic functions are also presented. Generalization of al inear differential operator D ; ; is introduced. Motivated by some results of Millerand Mocanu and other results of Bulboaca, differential super ordination and differential subordination are considered. Hankel determinant problem for the class of analytic functions defined by D ; ; is obtained. A generalization of linear operator denoted byL(m; `; ; a; c) is defined. A majorization of the class S (m; `; ; a; c; ) is obtained. The differential operator D ;s ; is introduced. Some properties belonging to this operator and new subclasses with respect to k-symmetric points are studied. A subclass of univalent functions with negative coefficients defined by D ;s ; shall be studied as well. By making use of the familiar concept of neighborhoods of analytic functions, several inclusion relations associated with the (n; )-neighborhoods of certain subclasses of analytic functions of operator D ; ; will be considered. A linear operator J ;a;c(; )involving the generalized of Hurwitz-Lerch zeta function for certain classes of analytic functions will be given. Several new subclasses will also be given for analytic functions defined by the operator J ;a;c(; ) and various properties are studied . Further, sufficient conditions for the univalence of an integral operator involving the generalized of Hurwitz-Lerch zeta function will be discussed. Lastly, new subclasses of harmonic functions with respect to k-symmetric points defined by D ;s ; will also be introduced and studied.,Ph.D. |
| Pages: | 117 |
| Call Number: | QA329.2.A254 2015 tesis |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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