A-Statistical Equal Approximation on Two Dimensional Weighted Spaces

Abstract

Korovkin type approximation theorems have very important role in the approximation theory. Many mathematicians investigate and improve these type of approximation theorems for various operators defined on different spaces via several new convergence methods. The convergence of a sequence of positive linear operators defined on weighted space was first studied by Gadjiev [Theorems of Korovkin type, Math. Zametki 20(1976), 781-786]. Then, these results were improved by many authors for different type of convergence methods. Recently, some authors study Korovkin type theorems for two variables functions by means of single and double sequences on weighted spaces. In this paper, we prove a Korovkin type approximation theorem for the notion of statistical equal convergence for double sequences on two dimensional weighted spaces. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. Also, we compute the rate of statistical equal convergence for double sequences on two dimensional weighted spaces.