This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and ...We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and Δ;, asusual, be the class of kth monotone functions.展开更多
The present note investigates the divergence phenomenon of copositive approximation by poiynomials in L'spaces. We show that the Jackson type estimates cannot hold, in general, for moduli of smoothness of higher d...The present note investigates the divergence phenomenon of copositive approximation by poiynomials in L'spaces. We show that the Jackson type estimates cannot hold, in general, for moduli of smoothness of higher degree.展开更多
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
基金Supported in part by Zhejiang Provincial Natural Science Foundation of Chinaa Special Research Fund ot" State Council of Education of China
文摘We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and Δ;, asusual, be the class of kth monotone functions.
文摘The present note investigates the divergence phenomenon of copositive approximation by poiynomials in L'spaces. We show that the Jackson type estimates cannot hold, in general, for moduli of smoothness of higher degree.
