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.
M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovi...M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:展开更多
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 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
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
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M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:
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 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.
