In the present paper, we give the explicit formula of the principal part of ∑k=0^n（{k}q-[n]qx）^sxk ∏m=0^n-k-1（1-q^mx） with respect to [n]q for any integer s and q ∈ （0, 1]. And, using the expressions, we obtai...In the present paper, we give the explicit formula of the principal part of ∑k=0^n（{k}q-[n]qx）^sxk ∏m=0^n-k-1（1-q^mx） with respect to [n]q for any integer s and q ∈ （0, 1]. And, using the expressions, we obtain saturation theorems for Bn （f , qn,x） approximating to f（x） ∈ C[O, 1], 0 〈 qn ≤ 1, qn → 1.展开更多
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
基金Supported by the National Natural Science Foundation (10601065)
文摘In the present paper, we give the explicit formula of the principal part of ∑k=0^n（{k}q-[n]qx）^sxk ∏m=0^n-k-1（1-q^mx） with respect to [n]q for any integer s and q ∈ （0, 1]. And, using the expressions, we obtain saturation theorems for Bn （f , qn,x） approximating to f（x） ∈ C[O, 1], 0 〈 qn ≤ 1, qn → 1.
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
