Equiconvergence of some sequences of rational functions

Abstract

The phenomenon of equiconvergence was first observed by Walsh for two sequences of polynomial interpolants to a class of functions. Here we obtain analogues of Yuanren's results for Walsh equiconvergence using rational functions as in Saff and Sharma. We extend this to Hermite interpolation and an earlier result of [1] is improved and corrected.

Keywords

• rational functions
• polynomials
• sequences
• interpolation
• equiconvergence.