r維近似算子的收斂速度; Convergence Rates of Some R-dimensional Approximation Operators for Vector-valued Function

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7797

Title:	r維近似算子的收斂速度;Convergence Rates of Some R-dimensional Approximation Operators for Vector-valued Function
Authors:	黃珮珊;Pei-Shan Huang
Contributors:	數學研究所
Keywords:	收斂速度;Korovkin;Bernstein-Type Operators
Date:	2001-06-26
Issue Date:	2009-09-22 11:05:40 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	本論文主要在討論某些r維近似算子對向量值函數的均勻收斂及估計它們的收斂速度。在第二節中，為求整篇論文的完整性，我們將所使用的兩個重要的Korovkin近似定理之證明再詳述一遍，以便下面幾節的應用。在第三到第七節中，我們分別考慮定義在兩種不同空間的五種r維算子，證明這些算子對向量值函數的均勻收斂及估計它們的收斂速度。最後，我們應用前面幾節所得到的近似結果，將向量值函數以半群函數代入，而得到一些半群的表示公式，但對於Durrmeyer Operators和Meyer-König and Zeller Operators是無法應用於半群表示的。 The purpose of this thesis is to study, by means of some r-dimensional linear operators, the approximation of vector-valued functions defined on a bounded subset. We use an approximation theorem of Korovkin type to prove that these operators converge uniformly, and then use another Korovkin-type theorem with rate to estimate their pointwise convergence rates. Finally, we apply some of these concrete approximation processes to derive some representation formulas for r-parameter semigroups of bounded linear operators.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

Files in This Item:

File	Size	Format

社群 sharing

Loading...