STATISTICAL KOROVKIN-TYPE THEORY FOR MATRIX-VALUED FUNCTIONS
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.48, no.4, pp.489-508, 2011 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 48 Issue: 4
- Publication Date: 2011
- Doi Number: 10.1556/sscmath.2011.1179
- Journal Name: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.489-508
- Keywords: A-statistical convergence, matrix-valued functions, linear positive operators, Korovkin theorem, modulus of continuity, A-statistical rates of approximation, CONVERGENCE, OPERATORS
- Gazi University Affiliated: Yes
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.