Statistical Korovkin-Type Theory for Matrix-Valued Functions

Abstract

In this paper, using the notion of A-statistical convergence from the summability theory, we obtain a Korovkin-type theorem for the approximation by means of matrix-valued linear positive operators. We show that our theorem is more applicable than the result introduced by S. Serra-Capizzano [A Korovkin based approximation of multilevel Toeplitz matrices (with rectangular unstructured blocks) via multilevel trigonometric matrix spaces, SIAM J. Numer. Anal., 36 (1999), 1831-1857]. Furthermore, we compute the A-statistical rates of out approximation.