Korovkin type theorem for functions of two variables via lacunary equistatistical convergence

M. Mursaleen

Abstract: 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, $\frac{x}{1-x}$, $\frac{y}{1-y}$, ${\left(\frac{x}{1-x}\right)}^2+{\left(\frac{y}{1-y}\right)}^2$.

Keywords: statistical convergence, lacunary equistatistical convergence, positive linear operator, Korovkin type approximation theorem

Classification (MSC2000): 41A10;41A25;41A36; 40A30;40G15

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