Korovkin type approximation theorems for weighted alpha beta-statistical convergence

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KARAKAYA V. , Karaisa A.

BULLETIN OF MATHEMATICAL SCIENCES, vol.5, no.2, pp.159-169, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1007/s13373-015-0065-y
  • Page Numbers: pp.159-169


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.