In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem c...In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.展开更多
The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.
The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the...The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.展开更多
Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new ...Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.展开更多
In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤...In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤α ≤ 2）,where ‖· ‖o, ‖· ‖2,Cλ^2 are defined in the paper. As for its applications, we have extended some results before this paper.展开更多
基金Supported by National Science Foundation of China（10571040）
文摘In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.
文摘The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.
文摘The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.
基金Supported by National Natural Science Foundation of China (No.60872161)Natural Science Foundation of Tianjin (No. 08JCYBJC09600)
文摘Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.
基金the National Natural Science Foundation of China （No. 10571040） the Natural Science Foundation of Hebei Province （No. A2004000137）+1 种基金 the Doctorial Fund of Education Department of Hebei Province （No. B2004118） the Doctorial Fund of Hebei Normal University （No. L2003B04）.
文摘In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤α ≤ 2）,where ‖· ‖o, ‖· ‖2,Cλ^2 are defined in the paper. As for its applications, we have extended some results before this paper.
