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
It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we...It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.展开更多
A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence the...A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence theorem is obtained.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.
文摘It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.
文摘A two dimensional Bernstein operators on C(S) is given by B n(f;x,y)=nk=0kj=0f(jn,kn)P n,k,j (x,y) where S{(x,y)｜0≤x≤y≤1},f∈C(S),P n,k,j (x,y)=n kk jx j(y-x) k-j (1-y) n-k and the aproximation equivalence theorem is obtained.
