A study in the theory of geometric functions of a complex variable
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 defi...
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my-unimap-772022022-11-25T01:23:03Z A study in the theory of geometric functions of a complex variable Muhammad Zaini, Ahmad, Dr. 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 Universiti Malaysia Perlis (UniMAP) Thesis en http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77202 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/3/license.txt 8a4605be74aa9ea9d79846c1fba20a33 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/1/Page%201-24.pdf 30ddf6cde3cb447e4ab9e1a7c9afe8bf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/2/Full%20text.pdf 5ec6574aa02916879fe888c62966c49b http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/4/Hiba%20Fawzi.pdf 726ffc73e53743489f03d67494e6773d Universiti Malaysia Perlis (UniMAP) Functions of complex variables Geometric function theory Institute of Engineering Mathematics |
| institution |
Universiti Malaysia Perlis |
| collection |
UniMAP Institutional Repository |
| language |
English |
| advisor |
Muhammad Zaini, Ahmad, Dr. |
| topic |
Functions of complex variables Geometric function theory |
| spellingShingle |
Functions of complex variables Geometric function theory A study in the theory of geometric functions of a complex variable |
| description |
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 |
| format |
Thesis |
| 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 |
| granting_institution |
Universiti Malaysia Perlis (UniMAP) |
| granting_department |
Institute of Engineering Mathematics |
| url |
http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77202/4/Hiba%20Fawzi.pdf |
| _version_ |
1776104249512427520 |