A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

Abstract

In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.

Keywords

• four dimensional matrix
• double sequence
• power series method
• statistical convergence
• computer graphics
• error of approximation