The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings
This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2...
Saved in:
Main Author: | |
---|---|
Format: | Thesis |
Language: | English |
Published: |
2017
|
Subjects: | |
Online Access: | http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf http://eprints.usm.my/47548/ |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
my.usm.eprints.47548 |
---|---|
record_format |
eprints |
spelling |
my.usm.eprints.47548 http://eprints.usm.my/47548/ The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings Mohammed Alarifi, Najla QA1 Mathematics (General) This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| < 1: All functions f ∈ U are univalent. In the first problem, the U -radius is determined for several classes of analytic functions. These include the classes of functions f satisfying the inequality Re f (z)=g(z) > 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1k 2017-10 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf Mohammed Alarifi, Najla (2017) The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings. PhD thesis, Universiti Sains Malaysia. |
institution |
Universiti Sains Malaysia |
building |
Hamzah Sendut Library |
collection |
Institutional Repository |
continent |
Asia |
country |
Malaysia |
content_provider |
Universiti Sains Malaysia |
content_source |
USM Institutional Repository |
url_provider |
http://eprints.usm.my/ |
language |
English |
topic |
QA1 Mathematics (General) |
spellingShingle |
QA1 Mathematics (General) Mohammed Alarifi, Najla The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
description |
This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four
research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| < 1: All functions f ∈ U are univalent. In the first problem, the U -radius is determined for several classes of analytic functions. These include the classes of functions f satisfying the inequality Re f (z)=g(z) > 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of
analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function
φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1k |
format |
Thesis |
author |
Mohammed Alarifi, Najla |
author_facet |
Mohammed Alarifi, Najla |
author_sort |
Mohammed Alarifi, Najla |
title |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
title_short |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
title_full |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
title_fullStr |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
title_full_unstemmed |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
title_sort |
u -radius and hankel determinant for analytic functions, and product of logharmonic mappings |
publishDate |
2017 |
url |
http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf http://eprints.usm.my/47548/ |
_version_ |
1681490232321507328 |
score |
13.1944895 |