Mathematics and Statistics Vol. 9(6), pp. 927 - 930
DOI: 10.13189/ms.2021.090608
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Derivation of New Degrees for Best COCUNP Weighted Approximation: II

Malik Saad Al-Muhja ^1,2,*, Habibulla Akhadkulov ^1,3, Nazihah Ahmad ^1
1 Department of Mathematics and statistics, School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, Malaysia
² Department of Mathematics and Computer Application, College of Sciences, University of Al-Muthanna, Iraq
³ Department of General and Exact Sciences, Tashkent State University of Economics, Uzbekistan

ABSTRACT

Approximation Theory is a branch of analysis and applied mathematics requiring that the approximation process preserves certain -shaped properties defined at a finite interval , such as convexity in all or parts of the interval. The (Co)convex and Unconstrained Polynomial (COCUNP) approximation is one of the key estimations of the approximation theory that Kopotun has recently raised for ten years. Numerous studies have been conducted on modern methods of weighted approximation to construct the best degree of approximation. In developing COCUNP a novel technique, the Lebesgue Stieltjes integral-i technique is used to resolve certain disadvantages, such as Riemann's integrable functions, which do not have the degree of the best approximation in norm space. In order to achieve the main goal, Derivation of New Degree (DOND) of the best COCUNP approximation was constructions. The theoretical results revealed that, in general, the new degrees of best approximation were able to smaller errors compared to the existing literature in the same estimating. In conclusion, this study has successfully developed DOND for the best (Co)convex Polynomial (COCP) weighted approximation.

KEYWORDS
Constrained and Unconstrained Approximation, (Co)convex Polynomial Approximation, Lebesgue Stieltjes Integral

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Malik Saad Al-Muhja , Habibulla Akhadkulov , Nazihah Ahmad , "Derivation of New Degrees for Best COCUNP Weighted Approximation: II," Mathematics and Statistics, Vol. 9, No. 6, pp. 927 - 930, 2021. DOI: 10.13189/ms.2021.090608.

(b). APA Format:
Malik Saad Al-Muhja , Habibulla Akhadkulov , Nazihah Ahmad (2021). Derivation of New Degrees for Best COCUNP Weighted Approximation: II. Mathematics and Statistics, 9(6), 927 - 930. DOI: 10.13189/ms.2021.090608.