Statistical e-Convergence of Double Sequences and its Application to Korovkin-Type Approximation Theorem for Functions of Two Variables

Sever Y., Talo Ö.

Iranian Journal of Science and Technology, Transaction A: Science, vol.41, no.3, pp.851-857, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s40995-016-0018-7
  • Journal Name: Iranian Journal of Science and Technology, Transaction A: Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.851-857
  • Keywords: Double sequence space, e-convergence, Korovkin-type approximation theorem, Positive linear operator, Statistical e-convergence
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, we have introduced the concept of statistical e-convergence and proved some fundamental properties of statistical e-convergence. In addition, we have introduced strongly e- | C10| -summability and examined the relationship between statistical e-convergence and strongly e- | C10| -summability of double sequences. Finally, we investigate a Korovkin-type approximation theorem for double sequences of positive linear operators on the space of all continuous real-valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version.