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Sz\`{a}sz-Mirakjan 算子拟中插式的点态逼近等价定理
引用本文: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.
作者姓名:郭顺生  张更生  刘丽霞
作者单位:河北师范大学数学与信息科学学院, 河北 石家庄 050016;河北师范大学数学与信息科学学院, 河北 石家庄 050016;河北师范大学数学与信息科学学院, 河北 石家庄 050016
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).
摘    要:Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szasz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus wφ^2r (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 ∈ CB0, ∞) by making use of the unified modulus wφ^2r(f, t) (0≤λ≤ 1).

关 键 词:点态逼近  拟插值  逼近性质  直接定理  光滑模  无线  收敛  函数
收稿时间:2007/5/17 0:00:00
修稿时间:1/2/2008 12:00:00 AM

Pointwise Approximation by Sz\`{a}sz-Mirakjan Quasi-Interpolants
GUO Shun Sheng,ZHANG Geng Sheng and LIU Li Xia.Pointwise Approximation by Sz\`{a}sz-Mirakjan Quasi-Interpolants[J].Journal of Mathematical Research with Applications,2009,29(4):629-638.
Authors:GUO Shun Sheng  ZHANG Geng Sheng and LIU Li Xia
Institution:Department of Mathematics, Hebei Normal University, Hebei 050016, China;Department of Mathematics, Hebei Normal University, Hebei 050016, China;Department of Mathematics, Hebei Normal University, Hebei 050016, China
Abstract: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 $f\in C_B0,\infty)$ by making use of the unified modulus $\omega^{2r}_{\varphi^{\lambda}}(f,t)$ $(0\le \lambda\le 1)$.
Keywords:Quasi-interpolants  Sz\`{a}sz-Mirakjan operator  equivalence theorem  Ditzian-Totik modulus  unified modulus  
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