Hermite-Fej ́er interpolation with non-uniform nodes on the unit circle

Abstract

This research paper examines Hermite-Fej ́er interpolation on the unit circle with non-uniformly dis- tributed nodes. The authors make two main contributions: they provide an explicit formula for the interpo- latory polynomial and prove a mean convergence of it is studied for analytic function within the unit disk. These findings advance our understanding of this interpolation method for irregularly spaced data points in circular domain.