Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the tes...Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the test functions 1 and x2. This type of modification enables better error estimation on the interval[＋√3/3,＋∞] than the classic ones. Finally, a Voronovskaya-type theoremfor these operators is also obtained.展开更多
In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp（1≤ p 〈＋∞）has been obtained.
This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that a...This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.展开更多
文摘Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the test functions 1 and x2. This type of modification enables better error estimation on the interval[＋√3/3,＋∞] than the classic ones. Finally, a Voronovskaya-type theoremfor these operators is also obtained.
基金Supported by the NNSF of China(10371080)Supported by the Educational Committee Foundation of Beijing(01KJ-101)
文摘In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp（1≤ p 〈＋∞）has been obtained.
基金the Foundation of the Education Department of Jiangsu Province(No.05KJB110001)
文摘This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.
