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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التفاصيل البيبلوغرافية
المؤلف الرئيسي:	Ng, Zhen Chuan
التنسيق:	أطروحة
اللغة:	English
منشور في:	2017
الموضوعات:	QA1 Mathematics (General)
الوصول للمادة أونلاين:	http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf
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id	my-usm-ep.47735
record_format	uketd_dc
spelling	my-usm-ep.477352020-10-23T09:45:25Z Bohr’s Inequality And Its Extensions 2017-11 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 http://eprints.usm.my/47735/ http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik (School of Mathematical Sciences)
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
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
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
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
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik (School of Mathematical Sciences)
publishDate	2017
url	http://eprints.usm.my/47735/1/BOHR%E2%80%99S%20INEQUALITY%20AND%20ITS%20EXTENSIONS.pdf%20cut.pdf
_version_	1747821822172200960

Bohr’s Inequality And Its Extensions

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