The Simultaneous Approximation Average Error Of Lagrange Interpolation On The1-fold Integrated Wiener Space

In this paper, for weighted approximation in Lp-norm, we determine strongly asymptotic or-ders for the average enors of both function approximation and derivative approximation by the Lagrange interpolation sequence which based on the extended Chebyshev nodes of the second kind on the1-fold integrated Wiener space. These results show that the average errors of both function approximation and derivative approximation by above mentioned Lagrange interpolation sequence are weakly equivalent to the average errors of the corresponding best polynomial approx-imation sequence for approximation in Lp-norm. In the sense of Information-Based Complexity, if permissible information functionals consist of standard information, then the average errors of both function approximation and derivative approximation by above mentioned interpolation sequence are weakly equivalent to the corresponding sequences of minimal average radii of nonadaptive information.