Give a direct theorem of uniform approximation by BaskakovDurrmeyer operators and its combinations mainly,and improve the results derived by Xuan Peicai to a general form by ω r φ λ (f,t)(0≤λ≤1,φ(x)=x(1+cx),c>0).
Use the Ditzian modulous of smoothness ω 2 φλ(f,t)(0≤λ≤1) to study the relation of the derivatives between Sikkema operators and the smoothness of the function it approximate, and a direct theorem between Sikkema operators and the Ditzian modulous of smoothness is obtained.
In the paper, the approximation strong -- type direct theorem and weak -- type inverse theorem are given for Sikkema operators in the space C[0, 1 ], thus its approximation characterization is obtained.
A class of two dimension Meyer - Konig and Zeller Opcrators is constructed, and its degree of approximation and direct theorem on continuous function space and a class of interpolation space are obtained.
The results obtained in this paper actually imply that the establishment of the direct theorem will result in the establishment of the inverse theorem for the modified higher Hermite-Fejer interpolation and the modified higher Hermite interpolation.
Using the equivalence relation between weighted K-functional and weighted modula of smoothness, a direct theorem and inverse theorem of the relation connected with derivatives of the Bernstein operators and the smoothness of functions are obtained.
The direct theorem of the theory of approximation of harmonic functions is established in the case of functions defined on a compact set, the complement of which with respect to ? is a John domain.
Direct Theorem about Approximation on a Family of Two Segments
A direct theorem for strictly convex domains in ?n
We prove a direct theorem for shape preservingLp-approximation, 0>amp;lt;p>amp;lt;∞, in terms of the classical modulus of smoothnessw2(f, tp1).
The sharpness of the rate of approximation by certain operators to the identity is considered in the sense that there exist smooth elements such that a rate (given by a direct theorem) cannot be improved.
In this paper, we study the approximation in Orlicz spaces by the operators K_n(f,x)=sum from k=0 to ∞m_(nk)(x)C_(nk)~(-1)integral from n=0 to 1(dx/x)m_(nk)(t)f(t)dt, where C_(nk)=integral from n=0 to 1(dx/x)m_(nk)(t)dt=(n+1)/((n+k+1)(n+k+2)) m_(nk)(x)=(_k~(n+k))_x~k(1-x)~(n+1) the direct theorem and saturative theorem are obtained.