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    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:[數學研究所] 博碩士論文

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