An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces gener...An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.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
文摘An inverse theorem for the best weighted polynomial approximation of a function in L<sub>w<sub>α</sub></sub><sup>p</sup>（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in L<sub>p</sub>（R）w<sub>λ</sub>, where w<sub>α</sub> is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and W<sub>λ</sub> is a Freud weight. For Ditzian-Totik K-functionals on L<sub>P</sub>（S）, 1≤P≤∞, we obtain a new equivalence expression.
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.
