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.
Highlights
The primary objective of this work is to establish a link between approximation theory and summability methods via four-dimensional matrices and construction of bivariate
When there is r,s a positive number E such that |$r,s | ≤ E for all (r, s) ∈ N2 = N × N, the double sequence is said to be bounded. As it is well known, every convergent single sequence is bounded whereas a convergent double sequence need not to be bounded
We focus on two summability methods including double sequences to prove Korovkin type theorems for the proposed operators
Summary
Kantorovich introduced a new process to approximate Lebesgue integrable real-valued functions defined on [0, 1]
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