【摘要】 <正>1引言首先给出L_p范数的定义.当p=∞时,我们定义L_∞为[-1,1]上本性有界可测函数组成的函数空间,其范数‖·‖_∞定义为■当1≤p<∞时,设ω（x）>0为（-1,1）上的连续可积函数,记L_p,ω为以ω为权的加权可积函数组成的函数空间,其范数‖·‖_p,ω定义为:■更多还原

【Abstract】 Let Cⁿ（[-1,1]） denote the space of the functions defined on the interval[-1,1] and having continuous derivatives up to n^th order.In the approximation problem by Lagrange interpolation polynomials,it is well known that the optimal n-1 Lagrange interpolation nodes for Cⁿ（[-1,1]） under the uniform norm L_∞ are the zeros of n^th Chebyshev polynomial.Recently,N.S.Hoang gave the optimal n-1 Lagrange interpolation nodes for Cⁿ（[-1,1]） under the uniform norm L_∞when the interval endpoints are also included in the interpolation node set.In this paper,we give the optimal n-1 Lagrange interpolation nodes for Cⁿ（[-1,1]）under the norm L_p（1≤p <∞）,and the optimal n-1 Lagrange interpolation nodes for C（[-1,1]） under the norm L_p（1≤p<∞） when the interval endpoints are also included in the interpolation node set.In addition,we corrected the optimal deviation given in a paper of Babave and Hoyotov.更多还原