Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights

Abstract

Let and let , where and is an even function. Then we can construct the orthonormal polynomials of degree for . In this paper for an even integer we investigate the convergence theorems with respect to the higher-order Hermite and Hermite-Fejér interpolation polynomials and related approximation process based at the zeros of . Moreover, for an odd integer , we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros of .

Higher order Hermite-Fejer Interpolation on the unit circle

“…A considerable number of papers on higher order Hermite-Fejér interpolation processes on real nodes have been published (see [11] and [14]). This motivated us to consider a higher order Hermite-Fejér interpolation problem on non-uniform set of complex nodes on the unit circle.…”