STATISTICAL KOROVKIN-TYPE THEORY FOR MATRIX-VALUED FUNCTIONS

DUMAN O., Erkus-Duman E.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, cilt.48, sa.4, ss.489-508, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 4
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1556/sscmath.2011.1179
  • Dergi Adı: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.489-508
  • Anahtar Kelimeler: A-statistical convergence, matrix-valued functions, linear positive operators, Korovkin theorem, modulus of continuity, A-statistical rates of approximation, CONVERGENCE, OPERATORS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.