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

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

M. Mursaleen

Department of Mathematics, Aligarh Muslim University, Aligarh, India

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, x 1+x, y 1+y, (x 1+x) 2 +(y 1+y) 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, x 1-x, y 1-y, (x 1-x) 2 +(y 1-y) 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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Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.

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