| 一类修正的和与积分混合型算子的$L_p$逼近 |
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| 引用本文： | 齐秋兰,郭顺生,李建坤.一类修正的和与积分混合型算子的$L_p$逼近[J].数学研究及应用,2009,29(6):1069-1081. |
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| 作者姓名： | 齐秋兰 郭顺生 李建坤 |
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| 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 |
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| 基金项目： | 国家自然科学基金(No.10571040). |
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| 摘 要： | The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.
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| 关 键 词： | Lp空间 求和函数 积分型 算子逼近 改性 运营商 有界变差 渐近公式 |
| 收稿时间： | 2007/10/5 0:00:00 |
| 修稿时间： | 7/7/2008 12:00:00 AM |
Approximation by Modified Summation Integral Type Operators in the $L_p$ Spaces |
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| QI Qiu Lan,GUO Shun Sheng and LI Jian Kun.Approximation by Modified Summation Integral Type Operators in the $L_p$ Spaces[J].Journal of Mathematical Research with Applications,2009,29(6):1069-1081. |
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| Authors: | QI Qiu Lan GUO Shun Sheng and LI Jian Kun |
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| Institution: | College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China;College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China;College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China |
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| Abstract: | The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the $L_p$ spaces. |
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| Keywords: | Beta operators $K$-functional moduli of smoothness Riesz-Thorin interpolation theorem H\"{o}lder inequality |
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