Weighted statistical convergence and its application to Korovkin type approximation theorem

Mursaleen M., Karakaya V., Erturk M., Gursoy F.

APPLIED MATHEMATICS AND COMPUTATION, cilt.218, sa.18, ss.9132-9137, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 218 Sayı: 18
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.amc.2012.02.068
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9132-9137
  • Anahtar Kelimeler: Density, Statistical convergence, Weighted statistical convergence, Statistical summability ((N)over-bar, p(n)), Positive linear operator, Korovkin type approximation theorem, SUMMABILITY
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The concept of weighted statistical convergence was introduced and studied by Karakaya and Chishti (2009) [7]. In this paper, we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability ((N) over bar, p(n)) due to Moricz and Orhan (2004) [10]. We apply this new summability method to prove a Korovkin type approximation theorem by using the test functions 1, e(-x), e(-2x). We apply the classical Baskakov operator to construct an example in support of our result. (C) 2012 Elsevier Inc. All rights reserved.