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
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
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
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.
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
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
文摘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.
基金Supported by the Key Academic Discipline of Zhejiang Provincial of China under Grant No.2005.
文摘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.
文摘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.
文摘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.
基金Supported by Foundation of Key Item of Science and Technology of Education Ministry of China (03142)Foundation of Higher School of Ningxia (JY2002107)Nature Science Foundation of Zhejiang Province(102002).
文摘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.
基金the National Natural Science Foundation of China (No.10571040)
文摘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.
