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Simultaneous Approximation by Baskakov-Durrmeyer Operator
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作者 齐秋兰 郭顺生 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第1期38-45,共8页
In this paper, we investigate the degree of approximation by Baskakov_Durrmeyer operator for functions which derivatives have only discontinuity points of the first kind on [0,∞) with exponential growth.
关键词 OPERATORS simultaneous approximation moduli of smoothness
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EQUIVALENT THEOREMS ON SIMULTANEOUS APPROXIMATION BY COMBINATIONS OF BERNSTEIN OPERATORES 被引量:1
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作者 Li Cheng Linsen Xie 《Analysis in Theory and Applications》 2006年第3期246-253,共8页
In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian- Totik modulus of smoothness w^rφλ (f, t)(0 ≤ λ≤ 1). We also investigate th... In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian- Totik modulus of smoothness w^rφλ (f, t)(0 ≤ λ≤ 1). We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions. 展开更多
关键词 Bernstein operators COMBINATION simultaneous approximation moduli of smoothness
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L^p APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX 被引量:1
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作者 CaoFeilong 《Analysis in Theory and Applications》 2004年第1期35-51,共17页
As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong di... As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived. 展开更多
关键词 general Bernstein-Durrmeyer operators direct theorem inverse theorem moduli of smoothness LP approximation
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K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex
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作者 Song Li Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第3期395-403,405-406,共11页
An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>(S) is established. We also investigate Besov spaces gener... An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>(R)w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>(S), 1≤P≤∞, we obtain a new equivalence expression. 展开更多
关键词 Weighted moduli of smoothness K-FUNCTIONAL Best weighted polynomial approximation SIMPLEX
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EQUIVALENT THEOREMS ON SIMULTANEOUS APPROXIMATION BY COMBINATIONSOF GAMMA OPERATORS
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作者 LiangchengMao Xueyan Xiang Wenshan Yang 《Analysis in Theory and Applications》 2008年第2期149-159,共11页
In this paper, some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωφλ^r(f,t)wφ^s(0≤λ≤1)are given. The relation between derivatives ... In this paper, some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωφλ^r(f,t)wφ^s(0≤λ≤1)are given. The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated. 展开更多
关键词 Gamma operator simultaneous approximation weighted moduli of smoothness
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Approximation by Modified Summation Integral Type Operators in the L_p Spaces 被引量:2
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作者 齐秋兰 郭顺生 李建坤 《Journal of Mathematical Research and Exposition》 CSCD 2009年第6期1069-1081,共13页
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 variati... 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. 展开更多
关键词 Beta operators K-FUNCTIONAL moduli of smoothness Riesz-Thorin interpolationtheorem H61der inequality.
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ON WAVELETS IN L_1
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作者 周定轩 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1994年第1期69-74,共6页
In this paper we give a method to characterize the smoothness of functions in L1 by an r-regular multiresolution analysis and its derivatives.
关键词 WAVELETS r-regular multiresolution analysis K-FUNCTIONAL moduli of smoothness
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