Asymptotic properties of iterates of certain positive linear operators

Mahmudov N.

Mathematical and Computer Modelling, vol.57, no.5-6, pp.1480-1488, 2013 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 57 Say: 5-6
  • Nəşr tarixi: 2013
  • Doi nömrəsi: 10.1016/j.mcm.2012.12.009
  • jurnalın adı: Mathematical and Computer Modelling
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.1480-1488
  • Açar sözlər: Bernstein operators, Cesaro operators, Degree of approximation, Genuine Bernstein-Durrmeyer operators, Iterates of operators, K-functionals, Korovkin type theorem, Meyer-Konig and Zeller operators, Modulus of smoothness, Stancu operators
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

In this paper we prove Korovkin type theorem for iterates of general positive linear operators T:C[0, 1]→C[0, 1] and derive quantitative estimates in terms of modulus of smoothness. In particular, we show that under some natural conditions the iterates Tm:C[0, 1]→C[0, 1] converges strongly to a fixed point of the original operator T. The results can be applied to several well-known operators; we present here the q-MKZ operators, the q-Stancu operators, the genuine q-Bernstein-Durrmeyer operators and the Cesaro operators. © 2012 Elsevier Ltd.