For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is th...For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.展开更多
In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to w...In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.展开更多
In this paper, some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωφλ^r（f,t）wφ^s（0≤λ≤1）are given. The relation between derivatives ...In this paper, some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωφλ^r（f,t）wφ^s（0≤λ≤1）are given. The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.展开更多
The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of p...The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of probability theory.展开更多
Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with...Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with ωφλ^2r（f,t）∞ by means of unified the classical modulus and Ditzian-Totick modulus.展开更多
基金Supported by the Hebei Provincial Natural Science Foundation of China(101090). Supported by the Major Subject Foundation of Hebei Normal University.
文摘For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.
文摘In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.
文摘In this paper, some equivalent theorems on simultaneous approximation for combinations of Gamma operators by weighted moduli of smoothness ωφλ^r（f,t）wφ^s（0≤λ≤1）are given. The relation between derivatives of combinations of Gamma operators and smoothness of derivatives of functions is also investigated.
文摘The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of probability theory.
基金the NSF of Zhejiang Province(102005)the Foundation of Key Discipline of ZhejiangProvince(2005)
文摘Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with ωφλ^2r（f,t）∞ by means of unified the classical modulus and Ditzian-Totick modulus.
