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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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主要作者: Al-Muhja, Malik Saad Abdalhassan
格式: Thesis
语言:English
English
出版: 2022
主题:
QA Mathematics
QA299.6-433 Analysis
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https://etd.uum.edu.my/9784/2/s902523_01.pdf
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spelling my.uum.etd.97842022-08-24T01:40:20Z https://etd.uum.edu.my/9784/ Best weighted approximation and its degree for (co) convex and unconstrained polynomials Al-Muhja, Malik Saad Abdalhassan 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 NonPeerReviewed text en https://etd.uum.edu.my/9784/1/permission%20to%20deposit-grant%20the%20permission-902523.pdf text en https://etd.uum.edu.my/9784/2/s902523_01.pdf Al-Muhja, Malik Saad Abdalhassan (2022) Best weighted approximation and its degree for (co) convex and unconstrained polynomials. Doctoral thesis, Universiti Utara Malaysia.
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Electronic Theses
url_provider http://etd.uum.edu.my/
language English
English
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
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
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
https://etd.uum.edu.my/9784/
_version_ 1743109563382497280
score 13.251813

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