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Statistical convergence and approximation theorems for functions of two variables. (English) Zbl 1275.41011

Summary: We use the notion of \((\lambda,\mu)\)-statistical convergence to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions \(1\), \(x\), \(y\), \(x^2+y^2\). Furthermore, we define a new type of summability method via \((\lambda,\mu)\)-statistical convergence and use it to prove a Korovkin-type theorem. Moreover, we obtain the order of \((\lambda,\mu)\)-statistical convergence in our approximation.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
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