The generalization of Meyer-Konig and Zeller operators by generating functions

Altin A., Dogru O., Tasdelen F.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.312, sa.1, ss.181-194, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 312 Sayı: 1
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1016/j.jmaa.2005.03.086
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.181-194
  • Anahtar Kelimeler: positive linear operators, Korovkin theorem, Meyer-Konig and zeller operators, modified Lipschitz class, K-functional of Peetre, modulus of continuity, Riccati differential equation, BERNSTEIN POWER-SERIES
  • Gazi Üniversitesi Adresli: Hayır

Özet

In this paper, theorems are proved concerned with some approximation properties of generating functions type Meyer-Konig and Zeller operators with the help of a Korovkin type theorem. Secondly, we compute the rates of convergence of these operators by means of the modulus of continuity, Peetre's K-functional and the elements of the modified Lipschitz class. Also we introduce the rth order generalization of these operators and we obtain approximation properties of them. In the last part, we give some applications to the differential equations. (c) 2005 Elsevier Inc. All rights reserved.