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SETSCI - Volume 4 (6) (2019)
ISAS WINTER-2019 (ENS) - 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences, Samsun, Turkey, Nov 22, 2019

A-Statistical Equal Approximation on Two Dimensional Weighted Spaces
Sevda Yıldız1*, Fadime Dirik2, Kamil Demirci3
1Sinop University, Sinop, Turkey
2Sinop University, Sinop, Turkey
3Sinop University, Sinop, Turkey
* Corresponding author: sevdaorhan@sinop.edu.tr
Published Date: 2019-12-22   |   Page (s): 185-192   |    261     13
https://doi.org/10.36287/setsci.4.6.055

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.  
KEYWORDS Double Sequences, Korovkin theorem, Statistical Equal Convergence, Weighted Spaces
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