The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturatio...The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well.展开更多
In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_...In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,H)(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.展开更多
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superi...In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.展开更多
The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^...The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2(S^q) norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics.展开更多
The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
Fructus cnidii (Chinese name shechuangzi) is the fruit produced by Cnidium monnieri (L.) Cusson (Umbelliferae). It is a perennial herb that is used to treat skin-related diseases and gynecopathyell. Recent pharm...Fructus cnidii (Chinese name shechuangzi) is the fruit produced by Cnidium monnieri (L.) Cusson (Umbelliferae). It is a perennial herb that is used to treat skin-related diseases and gynecopathyell. Recent pharmacological studies have revealed crude extracts or components isolated from fructus cnidii possess antiallergic, antipruritic, antidermatophytic, antibacterial, antifungal, and antiosteoporotic activities. Osthole and imperatorin are the major compounds present in shechuangzi. They are often used as standards for the evaluation of the quality of shechuangzi products.展开更多
In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.
文摘The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well.
文摘In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,H)(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
基金Supported by Science and Research Fund Item of Education Department of Zhejiang Province(20050408).
文摘For the nonpositive Hermite-Fejér interpolation based on the Laguerre abscissas, a pointwise two-sided estimate of the degree of approximation in the aleatoric interval [0, A] is first established.
基金This work is supported by the Natural Science Foundation of Zhejiang,PR China.
文摘In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.
基金Supported by the National Natural Science Foundation of China(No.10471130,10371024)the Natural Science Fund of Zhejiang Province(No:Y604003)
文摘The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2(S^q) norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics.
基金This work is supported by the Doctor Foundation (No:02.T20102-06) and the Post Doctor Foundation of Ningbo University.
文摘The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
基金Supported by the Talented Young Pressional Foundation of Jilin Province(No 2005123)
文摘Fructus cnidii (Chinese name shechuangzi) is the fruit produced by Cnidium monnieri (L.) Cusson (Umbelliferae). It is a perennial herb that is used to treat skin-related diseases and gynecopathyell. Recent pharmacological studies have revealed crude extracts or components isolated from fructus cnidii possess antiallergic, antipruritic, antidermatophytic, antibacterial, antifungal, and antiosteoporotic activities. Osthole and imperatorin are the major compounds present in shechuangzi. They are often used as standards for the evaluation of the quality of shechuangzi products.
基金Department of Mathematics and Statistics,Auburn University,AL,USA
文摘In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.