Continuity and Convergence Properties of Integral Means of Bojanov–Xu Interpolation

Abstract

We study Bojanov-Xu interpolation whose interpolation points are located on concentric circles in ${\mathbb{R}}^2$. We prove that the integral means of the interpolation polynomial over a fixed circle or a fixed annulus are continuous functions of the radii of circles. We also give a distribution of the radii such that the integral means are convergent.