There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function b...The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.展开更多
In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,k（Rd） by a subspace Ek2（σ） （SEk2（σ））, which is a subspace of entire functions of exponential type （spherical exponen...In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,k（Rd） by a subspace Ek2（σ） （SEk2（σ））, which is a subspace of entire functions of exponential type （spherical exponential type） at most σ. Here L2,k（Rd） denotes the space of all d-variate functions f endowed with the L2-norm with the weight vk（x）=Пζ∈R＋}（ζ,x）}2k（ζ）,which is defined by a positive subsystem R＋ of a finite root system R Rd and a function k（ζ）：R→R＋ invariant under the reflection group G（R） generated by R. In the case G（R） = Z2d, we get some exact results. Moreover, the deviation of best approximation by the subspace Ek2（σ） （SE2（σ）） of some class of the smooth functions in the space L2,k（Rd） is obtained.展开更多
The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function...The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.展开更多
文摘There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
基金supported by the Ningbo Youth Foundation(0 2 J0 1 0 2 - 2 1 )
文摘The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus.
基金Supported by National Natural Science Foundation of China(Grant No.11071019)the research Fund for the Doctoral Program of Higher Education and Beijing Natural Science Foundation(Grant No.1102011)
文摘In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,k（Rd） by a subspace Ek2（σ） （SEk2（σ））, which is a subspace of entire functions of exponential type （spherical exponential type） at most σ. Here L2,k（Rd） denotes the space of all d-variate functions f endowed with the L2-norm with the weight vk（x）=Пζ∈R＋}（ζ,x）}2k（ζ）,which is defined by a positive subsystem R＋ of a finite root system R Rd and a function k（ζ）：R→R＋ invariant under the reflection group G（R） generated by R. In the case G（R） = Z2d, we get some exact results. Moreover, the deviation of best approximation by the subspace Ek2（σ） （SE2（σ）） of some class of the smooth functions in the space L2,k（Rd） is obtained.
文摘The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.
