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
The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Di...The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness.展开更多
In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the...In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the Voronovskaja-type result for the operators.展开更多
We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by me...We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by means of the weighted modulus continuity and also obtain a Voronovskaya-type theorem. Furthermore, in our paper show that the operators give better degree of approximation of functions belonging to weighted spaces than classical Szaisz- Kantorovich operators.展开更多
Let ν be a finite Borel measure on[0,1]The Kantorovich-Stieltjes polynomials are de- fined by K_n ν=(n+1)N_(k,n)(nN), where N_(k,n)(x)=x^k(1-x)^(n-k)(x[0,1],k=1,2,…,n)are the basic Bernstein polynomials and I_(k,n)...Let ν be a finite Borel measure on[0,1]The Kantorovich-Stieltjes polynomials are de- fined by K_n ν=(n+1)N_(k,n)(nN), where N_(k,n)(x)=x^k(1-x)^(n-k)(x[0,1],k=1,2,…,n)are the basic Bernstein polynomials and I_(k,n):=[k/(n+1),(k+1)/(n+1)](k=0,1,…,n;nN).We prove that the maximal operator of the sequence(K_n)is of weak type and the sequence of polynomials(K_n ν)con- verges a.e.on[0,1]to the Radon-Nikodym derivative of the absolutely continuous part of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.
基金Supported by the foundation of Zhejiang province
文摘The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness.
基金Supported by the Natural Science Foundation of Beijing(1072006)Supported by NSFC(10871017)
文摘In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the Voronovskaja-type result for the operators.
文摘We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by means of the weighted modulus continuity and also obtain a Voronovskaya-type theorem. Furthermore, in our paper show that the operators give better degree of approximation of functions belonging to weighted spaces than classical Szaisz- Kantorovich operators.
基金the National Scientific Research Foundation(Grant No.384/324/0413)
文摘Let ν be a finite Borel measure on[0,1]The Kantorovich-Stieltjes polynomials are de- fined by K_n ν=(n+1)N_(k,n)(nN), where N_(k,n)(x)=x^k(1-x)^(n-k)(x[0,1],k=1,2,…,n)are the basic Bernstein polynomials and I_(k,n):=[k/(n+1),(k+1)/(n+1)](k=0,1,…,n;nN).We prove that the maximal operator of the sequence(K_n)is of weak type and the sequence of polynomials(K_n ν)con- verges a.e.on[0,1]to the Radon-Nikodym derivative of the absolutely continuous part of
