On Convergence of Hermite-Fejér Interpolation Polynomials Original Research Article

Hermite-Fejér interpolation operators based on the zeros of Jacobi polynomials, in general, are not uniformly convergent for all f ϵ C[−1, 1]. In this work we investigate weighted approximation by such operators with Jacobi weight functions. A necessary and sufficient condition for the weight function is given such that these interpolation polynomials converge in the weighted maximum norm for all f ϵ C[−1, 1].