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Statistical Korovkin-type theory for matrix-valued functions. (English) Zbl 1265.41053

The authors prove that the statistical Korovkin theory, improved by A. D. Gadjiev and C. Orhan [Rocky Mt. J. Math. 32, No. 1, 129–138 (2002; Zbl 1039.41018)] is also valid for the matrix-valued functions. First, they prove a Korovkin-type theorem for the \(A\)-statistical approximation of the mentioned functions (Theorem 2.1). Next, they compute the rate of \(A\)-statistical convergence using the modulus of continuity (Theorem 3.1, Theorem 3.2 and Theorem 4.1).

MSC:

41A36 Approximation by positive operators
41A25 Rate of convergence, degree of approximation
40G15 Summability methods using statistical convergence
65F35 Numerical computation of matrix norms, conditioning, scaling

Citations:

Zbl 1039.41018
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