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
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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