Saturation Problem ofLp-Approximation by Hermite–Fejér Interpolation Original Research Article

The saturation ofLp-approximation of Hermite–Fejér interpolation based on the zeros of generalized Jacobi polynomials is considered. Although mean convergence may improve the approximation order compared to uniform convergence, surprisingly, their saturation orders are exactly same, that is, 1/n. An inverse theorem is also given with respect toLp-approximation of Hermite–Fejér interpolation.