Korovkin type approximation theorems for weighted alpha beta-statistical convergence

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KARAKAYA V., Karaisa A.

BULLETIN OF MATHEMATICAL SCIENCES, cilt.5, sa.2, ss.159-169, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s13373-015-0065-y
  • Dergi Adı: BULLETIN OF MATHEMATICAL SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.159-169
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The concept of alpha beta-statistical convergence was introduced and studied by Aktu. glu (Korovkin type approximation theorems proved via alpha beta-statistical convergence, J Comput Appl Math 259: 174-181, 2014). In this work, we generalize the concept of alpha beta-statistical convergence and introduce the concept of weighted alpha beta-statistical convergence of order., weighted alpha beta-summability of order gamma, and strongly weighted alpha beta-summable sequences of order gamma. We also establish some inclusion relation, and some related results for these new summability methods. Furthermore, we prove Korovkin type approximation theorems through weighted alpha beta-statistical convergence and apply the classical Bernstein operator to construct an example in support of our result.