Necessary conditions to obtain Voronovskaja type asymptotic formulae via statistical limit

Dogru O.

12th WSEAS International Conference on APPLIED MATHEMATICS, Cairo, Mısır, 29 - 31 Aralık 2007, ss.128-129 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Basıldığı Şehir: Cairo
  • Basıldığı Ülke: Mısır
  • Sayfa Sayıları: ss.128-129
  • Anahtar Kelimeler: statistical convergence, Voronovskaja type asymptotic formulae, positive linear operators, APPROXIMATION THEOREMS, BERNSTEIN POLYNOMIALS, BASKAKOV OPERATORS, INVERSE THEOREMS, SZASZ
  • Gazi Üniversitesi Adresli: Hayır

Özet

It is well-known that, obtaining the necessary and sufficient conditions is not an easy task in the approximation theory. In a recent paper, necessary and sufficient conditions to obtain direct and inverse results for a sequence of general positive linear operators are given by us. Our results are valid for not only uniform approximation but also statistical approximation. On the other band, Voronovskaja obtained an asymptotic formulae to determine the order of uniform approximation of Bernstein polynomials to the function f. The main purpose of this paper is to give necessary conditions to obtain a Voronovskaja type asymptotic formulae for a sequence of general positive linear operators via statistical limit.