Generalized Bernstein-Kantorovich polynomials M_n^((k))(a_n, f, x) were introduced in the paper and their order of approximation were estimated in the L_p[0, 1]-spaces.
For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiene...For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space.By this result,it is known that in the sense of information-based complexity,if permissible information functionals are Hermite data,then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.展开更多
文摘Generalized Bernstein-Kantorovich polynomials M_n^((k))(a_n, f, x) were introduced in the paper and their order of approximation were estimated in the L_p[0, 1]-spaces.
文摘For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space.By this result,it is known that in the sense of information-based complexity,if permissible information functionals are Hermite data,then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.
