Max-product Shepard operators based on multivariable Taylor polynomials

Abstract

In this paper, by using multivariable Taylor polynomials and also the max-product operation, we give a nonlinear modification of the classical Shepard operators. This modification enables us to obtain better approximation behavior than the classical aspects studied by Shepard (1968) and Farwig (1986). We also discuss the effects of regular summability methods in the approximation. At the end of the paper, we give some applications and graphical simulations verifying our approximation results.