The combined Shepard-Abel-Goncharov univariate operator

Abstract

We extend the Shepard operator by combining it with the Abel-Goncharov univariate operator in order to increase the degree of exactness and to use some specific functionals. We study this combined operator and give some of its properties. We introduce the corresponding interpolation formula and study its remainder term.

Keywords

• Shepard-Abel-Goncharov operators
• interpolation formula
• degree of exactness
• remainder term