Best weighted approximation and its degree for (co) convex and unconstrained polynomials

Approximation theory is a branch of analysis and applied mathematics that approximates a function f which is defined on a finite interval [a,b] with preserving certain intrinsic shape properties and known as concavities of the functions. The study of (co)convex and unconstrained polynomial (COCUNP)...

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Main Author:	Al-Muhja, Malik Saad Abdalhassan
Format:	Thesis
Language:	eng eng
Published:	2022
Subjects:	QA Mathematics QA299.6-433 Analysis
Online Access:	https://etd.uum.edu.my/9784/1/permission%20to%20deposit-grant%20the%20permission-902523.pdf https://etd.uum.edu.my/9784/2/s902523_01.pdf
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spelling	my-uum-etd.97842022-08-24T01:40:20Z Best weighted approximation and its degree for (co) convex and unconstrained polynomials 2022 Al-Muhja, Malik Saad Abdalhassan Ahadkulov, Habibulla Ahmad, Nazihah Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Art & Sciences QA Mathematics QA299.6-433 Analysis Approximation theory is a branch of analysis and applied mathematics that approximates a function f which is defined on a finite interval [a,b] with preserving certain intrinsic shape properties and known as concavities of the functions. The study of (co)convex and unconstrained polynomial (COCUNP) are the important properties in finding the best approximation of a function. Numerous studies have been conducted using COCUNP approximation to construct a degree of the best approximation, but it depended on the Ditzian-Totik modulus of smoothness (DTMS) of f and also limited to a uniform norm space. Moreover, this approach could not be extended to the best weighted approximation of functions in general abstract spaces. Thus, to overcome this shortcoming, this study established a new symmetric difference using properties of Lebesgue Stieltjes integral-i which is called generalization of symmetric difference. Then, the best weighted approximation known as weighted DTMS is developed by taking the supremum of generalization of symmetric difference. In addition, new degrees of best (co)convex and unconstrained polynomial approximation are constructed using the proposed weighted DTMS. The result shows that the new approach is able to extend the best weighted approximation of functions in general abstract spaces. In addition, the weighted approximation by (co)convex polynomial provided a better accuracy compared to unconstrained polynomial. In conclusion, this study has successfully established the best weighted approximation and improved its degrees for (co)convex polynomial and COCUNP. 2022 Thesis https://etd.uum.edu.my/9784/ https://etd.uum.edu.my/9784/1/permission%20to%20deposit-grant%20the%20permission-902523.pdf text eng staffonly https://etd.uum.edu.my/9784/2/s902523_01.pdf text eng public other doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Ahadkulov, Habibulla Ahmad, Nazihah
topic	QA Mathematics QA299.6-433 Analysis
spellingShingle	QA Mathematics QA299.6-433 Analysis Al-Muhja, Malik Saad Abdalhassan Best weighted approximation and its degree for (co) convex and unconstrained polynomials
description	Approximation theory is a branch of analysis and applied mathematics that approximates a function f which is defined on a finite interval [a,b] with preserving certain intrinsic shape properties and known as concavities of the functions. The study of (co)convex and unconstrained polynomial (COCUNP) are the important properties in finding the best approximation of a function. Numerous studies have been conducted using COCUNP approximation to construct a degree of the best approximation, but it depended on the Ditzian-Totik modulus of smoothness (DTMS) of f and also limited to a uniform norm space. Moreover, this approach could not be extended to the best weighted approximation of functions in general abstract spaces. Thus, to overcome this shortcoming, this study established a new symmetric difference using properties of Lebesgue Stieltjes integral-i which is called generalization of symmetric difference. Then, the best weighted approximation known as weighted DTMS is developed by taking the supremum of generalization of symmetric difference. In addition, new degrees of best (co)convex and unconstrained polynomial approximation are constructed using the proposed weighted DTMS. The result shows that the new approach is able to extend the best weighted approximation of functions in general abstract spaces. In addition, the weighted approximation by (co)convex polynomial provided a better accuracy compared to unconstrained polynomial. In conclusion, this study has successfully established the best weighted approximation and improved its degrees for (co)convex polynomial and COCUNP.
format	Thesis
qualification_name	other
qualification_level	Doctorate
author	Al-Muhja, Malik Saad Abdalhassan
author_facet	Al-Muhja, Malik Saad Abdalhassan
author_sort	Al-Muhja, Malik Saad Abdalhassan
title	Best weighted approximation and its degree for (co) convex and unconstrained polynomials
title_short	Best weighted approximation and its degree for (co) convex and unconstrained polynomials
title_full	Best weighted approximation and its degree for (co) convex and unconstrained polynomials
title_fullStr	Best weighted approximation and its degree for (co) convex and unconstrained polynomials
title_full_unstemmed	Best weighted approximation and its degree for (co) convex and unconstrained polynomials
title_sort	best weighted approximation and its degree for (co) convex and unconstrained polynomials
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2022
url	https://etd.uum.edu.my/9784/1/permission%20to%20deposit-grant%20the%20permission-902523.pdf https://etd.uum.edu.my/9784/2/s902523_01.pdf
_version_	1747828671681396736

Best weighted approximation and its degree for (co) convex and unconstrained polynomials

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