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 we set up quanttative shisha-Mond type theorem of probability expression of (C0)-semigroup of opertors and we give an example by introducing S-λ probability distribution to ob-tain corresponding quantit...In this paper we set up quanttative shisha-Mond type theorem of probability expression of (C0)-semigroup of opertors and we give an example by introducing S-λ probability distribution to ob-tain corresponding quantitative estimation.展开更多
This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method f...This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.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.
文摘In this paper we set up quanttative shisha-Mond type theorem of probability expression of (C0)-semigroup of opertors and we give an example by introducing S-λ probability distribution to ob-tain corresponding quantitative estimation.
文摘This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W2m spaces, The explicit constructive method for the reproducing kernel in W2m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W2m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W2m space, and error estimation of spline operator of approximation are obtained.
