Publications de l’Institut Mathématique, Nouvelle Série Vol. 102[116], pp. 203–209 (2017) 

Korovkin type theorem for functions of two variables via lacunary equistatistical convergenceM. MursaleenDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaAbstract: Aktuğlu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and Gönül [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, $\frac{x}{1+x}$, $\frac{y}{1+y}$, ${\left(\frac{x}{1+x}\right)}^{2}+{\left(\frac{y}{1+y}\right)}^{2}$. We apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem for functions of two variables by using test functions 1, $\frac{x}{1x}$, $\frac{y}{1y}$, ${\left(\frac{x}{1x}\right)}^{2}+{\left(\frac{y}{1y}\right)}^{2}$. Keywords: statistical convergence, lacunary equistatistical convergence, positive linear operator, Korovkin type approximation theorem Classification (MSC2000): 41A10;41A25;41A36; 40A30;40G15 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.
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