郭顺生,张更生,刘丽霞.Sz\`{a}sz-Mirakjan 算子拟中插式的点态逼近等价定理[J].数学研究及应用,2009,29(4):629~638 |
Sz\`{a}sz-Mirakjan 算子拟中插式的点态逼近等价定理 |
Pointwise Approximation by Sz\`{a}sz-Mirakjan Quasi-Interpolants |
投稿时间:2007-05-17 修订日期:2008-01-02 |
DOI:10.3770/j.issn:1000-341X.2009.04.008 |
中文关键词: 拟中插式 Sz\`{a}sz-Mirakjan 算子 等价定理 Ditzian-Totik 光滑模 统一光滑模. |
英文关键词:Quasi-interpolants Sz\`{a}sz-Mirakjan operator equivalence theorem Ditzian-Totik modulus unified modulus. |
基金项目:国家自然科学基金(No.10571040); 河北师范大学博士基金(No.L2004B04). |
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中文摘要: |
最近人们引入了著名算子的拟中插式,以期得到更快的逼近速度. A.T.Diallo 研究了Sz\`{a}sz-Mirakjan算子的拟中插式 的一些逼近性质, 但是他只是利用Ditzian-Totik光滑模$\omega^{2r}_{\varphi}(f,t)$获得了逼近正定理. 我们利用统一光滑模 $\omega^{2r}_{\varphi^{\lambda}}(f,t)$ $(0\le \lambda\le 1)$完全刻画了这类算子的逼近性质, 涵盖了 Diallo 的结论. |
英文摘要: |
Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Sz\`{a}sz-Mirakjan Quasi--Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus $\omega^{2r}_{\varphi}(f,t)$. In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions $f\in C_B[0,\infty)$ by making use of the unified modulus $\omega^{2r}_{\varphi^{\lambda}}(f,t)$ $(0\le \lambda\le 1)$. |
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