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Title:	On certain classes of univalent and multivalent functions related to meromorphic type
Authors:	Mostafa Taher Ali Albehbah (P68838)
Supervisor:	Maslina Darus, Prof. Dr.
Keywords:	Geometric function theory
Issue Date:	30-Jul-2017
Description:	This thesis focuses on two major classes of functions in Geometric Function Theory, namely, the class of univalent functions and the class of multivalent functions. Both of the classes are related to a meromorphic type. Some subclasses defined by a differential operator involving basic hypergeometric functions are given. Basic definitions and initial results are stated. For the class of meromorphic univalent functions, a differential operator is introduced. By using this operator, certain new subclasses of meromorphic univalent functions with positive coefficients in the punctured unit disc are defined followed by their properties such as coefficient estimates, convex linear combinations, distortion theorems, and radii of starlikeness and convexity. Furthermore, a study on the same properties of the new subclasses of multivalent meromorphic functions by generalising the previous operator is given. Next, a class of meromorphic multivalent functions with positive coefficient is introduced by generalising the particular differential operator in the same space. Coefficient estimates, distortion theorem, radii of convexity, closure theorems and integral transforms for this class are obtained. Also, by employing the concept of the convolution and subordination some subordination results for certain family of meromorphic prevalent functions are studied. In addition, new subclasses of meromorphic univalent functions with fixed second positive coefficient are defined based on the previous differential operator involving hypergeometric functions. Here, several properties such as the coefficient estimates, convex linear combinations, distortion theorems, and radii of starlikeness and convexity are obtained. Moreover, the Convolution technique is employed to introduce a general operator involving the basic hypergeometric functions. By utilising this operator, some subclasses of hypergeometric meromorphic multivalent functions are defined. Further, sufficient conditions, distortion properties and radii of starlikeness and convexity are obtained. Finally, two subclasses of meromorphic multivalent functions involving the generalised hypergeometric functions are introduced. Some properties are studied and the neighbourhood concept is extended to this class. Other results associated with Hadamard product are also derived.,Certification of Master's/Doctoral Thesis" is not available
Pages:	111
Call Number:	QA331.7.A434 2017 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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