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A study in the theory of geometric functions of a complex variable

Doctor of Philosophy in Pure Mathematics

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Bibliographic Details
Main Author: Hiba Fawzi Sabba, Al-Janaby
Other Authors: Muhammad Zaini, Ahmad, Dr.
Format: Thesis
Language:English
Published: Universiti Malaysia Perlis (UniMAP) 2016
Subjects:
Functions of complex variables
Geometric function theory
Online Access:http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77202
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spelling my.unimap-772022022-11-25T01:23:03Z A study in the theory of geometric functions of a complex variable Hiba Fawzi Sabba, Al-Janaby Muhammad Zaini, Ahmad, Dr. Functions of complex variables Geometric function theory Doctor of Philosophy in Pure Mathematics This thesis deals with various types of analytic geometric functions in the open unit disk, such as normalized, meromorphic, p-valent, harmonic, and fractional analytic functions. Five problems are discussed. First, the class of analytic functions of fractional power is suggested and used to define a generalized fractional differential operator, which corresponds to the Srivastava–Owa operator. The upper and lower bounds for fractional analytic functions containing this operator are discussed by employing the first-order subordination and superordination. Coefficient bounds for the new subclass of multivalent ( p-valent) analytic functions containing a certain linear operator are then presented. Other geometric properties of this class are studied. A new subclass of meromorphic valent functions defined by subordination and convolution is also established, and some of its geometric properties are studied. For a normalized function, the extended Gauss hypergeometric functions, which are generalized integral operators involving the Noor integral operator, are posed and examined. New subclasses of analytic functions containing the generalized integral operator are defined and established. In addition, some sandwich results are obtained. Third-order differential subordination outcomes for the linear operator convoluting the fractional integral operator with the incomplete beta function related to the Gauss hypergeometric function, are investigated. The dual concept of the third-order differential superordination is also considered to obtain third-order differential sandwich-type outcomes. Results are acquired by determining the appropriate classes of admissible functions for third-order differential functions. The final phase of this dissertation introduces two subclasses of S'h , which are denoted by LH(r) and H(a,B) . Coefficient bounds, extreme points, convolution, convex combinations, and closure under an integral operator are investigated for harmonic univalent functions in the subclasses H(a,B) and Lh (r) . Connections between harmonic univalent and hypergeometric functions are also fully investigated 2016 2022-11-25T01:21:19Z 2022-11-25T01:21:19Z Thesis http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77202 en Universiti Malaysia Perlis (UniMAP) Universiti Malaysia Perlis (UniMAP) Institute of Engineering Mathematics
institution Universiti Malaysia Perlis
building UniMAP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Perlis
content_source UniMAP Library Digital Repository
url_provider http://dspace.unimap.edu.my/
language English
topic Functions of complex variables
Geometric function theory
spellingShingle Functions of complex variables
Geometric function theory
Hiba Fawzi Sabba, Al-Janaby
A study in the theory of geometric functions of a complex variable
description Doctor of Philosophy in Pure Mathematics
author2 Muhammad Zaini, Ahmad, Dr.
author_facet Muhammad Zaini, Ahmad, Dr.
Hiba Fawzi Sabba, Al-Janaby
format Thesis
author Hiba Fawzi Sabba, Al-Janaby
author_sort Hiba Fawzi Sabba, Al-Janaby
title A study in the theory of geometric functions of a complex variable
title_short A study in the theory of geometric functions of a complex variable
title_full A study in the theory of geometric functions of a complex variable
title_fullStr A study in the theory of geometric functions of a complex variable
title_full_unstemmed A study in the theory of geometric functions of a complex variable
title_sort study in the theory of geometric functions of a complex variable
publisher Universiti Malaysia Perlis (UniMAP)
publishDate 2016
url http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77202
_version_ 1753972994232811520
score 13.211869

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