Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
The present paper proves that if（x） ∈ C[0,1], changes its sign exactly l times at 0 〈 y1〈 y2 … 〈 y1 〈 1 in （0, 1）, then there exists a pn（x） ∈ Пn（＋）, such that ｜f（x）- p（x）/pn（x）｜≤ Cωφ（f,n^...The present paper proves that if（x） ∈ C[0,1], changes its sign exactly l times at 0 〈 y1〈 y2 … 〈 y1 〈 1 in （0, 1）, then there exists a pn（x） ∈ Пn（＋）, such that ｜f（x）- p（x）/pn（x）｜≤ Cωφ（f,n^（-1/2））, where ρ（x） is defined by ρ（x）={^lПi=1（x-yi）,if f （x）≥0 for x ∈（y1,1）, {-^lПi=1（x-yi）,if f （x）〈0 for x ∈（y1,1）, which improves and generalizes the result of .展开更多
基金Supported by the National Natural Science Foundation of China (1057104010801043)+1 种基金Natural Science Foundation of Hebei Province (08M001)Foundation of Education Department of Hebei Province (2008126)
文摘Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
基金Supported in part by National Natural Science Foundations of China under the grant number 10471130
文摘The present paper proves that if（x） ∈ C[0,1], changes its sign exactly l times at 0 〈 y1〈 y2 … 〈 y1 〈 1 in （0, 1）, then there exists a pn（x） ∈ Пn（＋）, such that ｜f（x）- p（x）/pn（x）｜≤ Cωφ（f,n^（-1/2））, where ρ（x） is defined by ρ（x）={^lПi=1（x-yi）,if f （x）≥0 for x ∈（y1,1）, {-^lПi=1（x-yi）,if f （x）〈0 for x ∈（y1,1）, which improves and generalizes the result of .
