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Bohr’s Inequality And Its Extensions

This thesis focuses on generalizing the Bohr’s theorem. Let h be a univalent function defined on U. Also, let R(a; g;h) be the class of functions f analytic in U such that the differential f (z)+az f 0(z)+gz2 f 00(z) is subordinate to h(z). The Bohr’s theorems for the class R(a; g;h) are proved for...

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主要作者:	Ng, Zhen Chuan
格式:	Thesis
语言:	English
出版:	2017
主题:	QA1 Mathematics (General)
在线阅读:	http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf http://eprints.usm.my/47735/
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id	my.usm.eprints.47735
record_format	eprints
spelling	my.usm.eprints.47735 http://eprints.usm.my/47735/ Bohr’s Inequality And Its Extensions Ng, Zhen Chuan QA1 Mathematics (General) This thesis focuses on generalizing the Bohr’s theorem. Let h be a univalent function defined on U. Also, let R(a; g;h) be the class of functions f analytic in U such that the differential f (z)+az f 0(z)+gz2 f 00(z) is subordinate to h(z). The Bohr’s theorems for the class R(a; g;h) are proved for h being a convex function and a starlike function with respect to h(0). The Bohr’s theorems for the class of analytic functions mapping U into concave wedges and punctured unit disk are next obtained in the following chapter. The classical Bohr radius 1=3 is shown to be invariant by replacing the Euclidean distance d with either the spherical chordal distance or the distance in Poincaré disk model. Also, the Bohr’s theorem for any Euclidean convex set is shown to have its analogous version in the Poincaré disk model. Finally, the Bohr’s theorems are obtained for some subclasses of harmonic and logharmonic mappings defined on the unit disk U. 2017-11 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf Ng, Zhen Chuan (2017) Bohr’s Inequality And Its Extensions. 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) Ng, Zhen Chuan Bohr’s Inequality And Its Extensions
description	This thesis focuses on generalizing the Bohr’s theorem. Let h be a univalent function defined on U. Also, let R(a; g;h) be the class of functions f analytic in U such that the differential f (z)+az f 0(z)+gz2 f 00(z) is subordinate to h(z). The Bohr’s theorems for the class R(a; g;h) are proved for h being a convex function and a starlike function with respect to h(0). The Bohr’s theorems for the class of analytic functions mapping U into concave wedges and punctured unit disk are next obtained in the following chapter. The classical Bohr radius 1=3 is shown to be invariant by replacing the Euclidean distance d with either the spherical chordal distance or the distance in Poincaré disk model. Also, the Bohr’s theorem for any Euclidean convex set is shown to have its analogous version in the Poincaré disk model. Finally, the Bohr’s theorems are obtained for some subclasses of harmonic and logharmonic mappings defined on the unit disk U.
format	Thesis
author	Ng, Zhen Chuan
author_facet	Ng, Zhen Chuan
author_sort	Ng, Zhen Chuan
title	Bohr’s Inequality And Its Extensions
title_short	Bohr’s Inequality And Its Extensions
title_full	Bohr’s Inequality And Its Extensions
title_fullStr	Bohr’s Inequality And Its Extensions
title_full_unstemmed	Bohr’s Inequality And Its Extensions
title_sort	bohr’s inequality and its extensions
publishDate	2017
url	http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf http://eprints.usm.my/47735/
_version_	1681490255794929664
score	13.251813

Bohr’s Inequality And Its Extensions

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