Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the per...In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.展开更多
The aim of this paper is to give direct and converse theorems for the approximation by using a discretely defined method Ln (see D. H. Mache [10], which is a modification of the Lagrange operator. Furthermore we obtai...The aim of this paper is to give direct and converse theorems for the approximation by using a discretely defined method Ln (see D. H. Mache [10], which is a modification of the Lagrange operator. Furthermore we obtain with a matrix construction technique (see M. D. Ye and D. X. Zhou [11]) a Lagrange-type operator n, for which we get a characterization for Lipschitz functions by the approximation rate of these methods.展开更多
We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.
In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1&...In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.展开更多
For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,...For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,y2 E∈if max{d(y1,go),d(y2,go)}=inf g∈K max{d(y1,g),d(y2,g)}.In this paper,some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved.For self mappings T and S on K,results are proved on both T-and S-invariant points for a set of best simultaneous approximation.Some results on best K-approximant are also deduced.The results proved generalize and extend some results of I.Beg and M.Abbas^[1],S.Chandok and T.D.Narang^[2],T.D.Narang and S.Chandok^[11],S.A.Sahab,M.S.Khan and S.Sessa^[14],P.Vijayaraju^[20]and P.Vijayaraju and M.Marudai^[21].展开更多
"Formulate the company's development strategy with an international perspective,and build core competitiveness with digital reform and intellectual transformation."Faced with the current complex and seve..."Formulate the company's development strategy with an international perspective,and build core competitiveness with digital reform and intellectual transformation."Faced with the current complex and severe international environment and the pressure of weak market demand,business operations must be planned from a high point with a new thinking operation.Jiang Zhongwei,Chairman of Best Garment Group is deeply aware that the only way to enhance competitiveness,open a new pattern,and achieve a new future is to continuously cultivate new quality productivity,take the global market as the guider,and push forward the systematic innovation of the whole production factors.展开更多
The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best app...The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's condition.Some recent results due to Lewicki and others are extended and improved.展开更多
In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and ...In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.展开更多
文摘Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
文摘In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.
基金The second author is supported by the Alexander von Humboldt-Stiftung.
文摘The aim of this paper is to give direct and converse theorems for the approximation by using a discretely defined method Ln (see D. H. Mache [10], which is a modification of the Lagrange operator. Furthermore we obtain with a matrix construction technique (see M. D. Ye and D. X. Zhou [11]) a Lagrange-type operator n, for which we get a characterization for Lipschitz functions by the approximation rate of these methods.
基金Supported by Education Foundation of Henan Province(200510463024)Supported by the Foundation of Henan University of Technology(20050206)
文摘We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.
文摘In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.
文摘For a subset K of a metric space(X,d)and x∈X,Px(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}is called the set of best K-approximant to x.An element go E K is said to be a best simulta-neous approximation of the pair y1,y2 E∈if max{d(y1,go),d(y2,go)}=inf g∈K max{d(y1,g),d(y2,g)}.In this paper,some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved.For self mappings T and S on K,results are proved on both T-and S-invariant points for a set of best simultaneous approximation.Some results on best K-approximant are also deduced.The results proved generalize and extend some results of I.Beg and M.Abbas^[1],S.Chandok and T.D.Narang^[2],T.D.Narang and S.Chandok^[11],S.A.Sahab,M.S.Khan and S.Sessa^[14],P.Vijayaraju^[20]and P.Vijayaraju and M.Marudai^[21].
文摘"Formulate the company's development strategy with an international perspective,and build core competitiveness with digital reform and intellectual transformation."Faced with the current complex and severe international environment and the pressure of weak market demand,business operations must be planned from a high point with a new thinking operation.Jiang Zhongwei,Chairman of Best Garment Group is deeply aware that the only way to enhance competitiveness,open a new pattern,and achieve a new future is to continuously cultivate new quality productivity,take the global market as the guider,and push forward the systematic innovation of the whole production factors.
基金This work was supported in part by the National Natural Science foundations of China (Grant No 10271025).
文摘The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's condition.Some recent results due to Lewicki and others are extended and improved.
基金supported partly by National Natural Science Foundation of China(GrantNo.11071019)Research Fund for the Doctoral Program of Higher Education and Beijing Natural Science Foundation(Grant No.1102011)
文摘In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.
