Korovkin type approximation theorem for functions of two variables in statistical sense

Authors

FADİME DİRİK
KAMİL DEMİRCİ

DOI

10.3906/mat-0802-21

Abstract

In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.

Keywords

A-Statistical convergence of double sequence, Korovkin-type approximation theorem, Bernstein polynomials, Voronovskaya-type theorem.

First Page

73

Last Page

84

Recommended Citation

DİRİK, FADİME and DEMİRCİ, KAMİL (2010) "Korovkin type approximation theorem for functions of two variables in statistical sense," Turkish Journal of Mathematics: Vol. 34: No. 1, Article 7. https://doi.org/10.3906/mat-0802-21
Available at: https://journals.tubitak.gov.tr/math/vol34/iss1/7