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...

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Main Author:	Mohammed Alarifi, Najla
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf
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spelling	my-usm-ep.475482020-10-14T08:04:30Z The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings 2017-10 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 http://eprints.usm.my/47548/ http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik (School of Mathematical Engineering)
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
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
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
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
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik (School of Mathematical Engineering)
publishDate	2017
url	http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf
_version_	1747821800207679488

The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings

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