On statistical convergence of difference sequences of fractional order and related Korovkin type approximation theorems

Baliarsingh P., Kadak U., Mursaleen M.

QUAESTIONES MATHEMATICAE, cilt.41, sa.8, ss.1117-1133, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 8
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2989/16073606.2017.1420705
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1117-1133
  • Anahtar Kelimeler: Statistical convergence of difference sequences, Korovkin type approximation theorems, linear operators, rates of convergence, SPACES, OPERATOR, DOMAIN, (P
  • Gazi Üniversitesi Adresli: Evet

Özet

Prior to investigating on sequence spaces and their convergence, we study the notion of statistical convergence of difference sequences of fractional order alpha is an element of Double-struck capital R. As generalizations of previous works, this study includes several special cases under different limiting conditions of alpha, such as the notion of statistical convergence of difference sequences of zeroth and mth (integer) order. In fact, we study certain new results on statistical convergence via the difference operator Delta(alpha) and interpret them to those of previous works. Also, by using the convergence of Delta(alpha)-summable sequences which is stronger than statistical convergence of difference sequences, we apply classical Bernstein operator and a generalized form of Meyer-Konig and Zeller operator to construct an example in support of our result. Also, we study the rates of Delta(alpha)-statistical convergence of positive linear operators.