On Statistical e-Convergence of Double Sequences

Sever Y., Talo Ö.

Iranian Journal of Science and Technology, Transaction A: Science, vol.42, no.4, pp.2063-2068, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s40995-017-0476-6
  • Journal Name: Iranian Journal of Science and Technology, Transaction A: Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2063-2068
  • Keywords: Double sequence space, e-convergence, Korovkin-type approximation theorem, Positive linear operator, statistical e-convergence
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

The concept of statistical e-convergence for a double sequence has been defined by Sever and Talo (Iran J Sci Technol Trans A Sci 41(3):851–857, 2017). In this paper we keep working on this convergence. We introduce the concepts of statistical e-limit superior and inferior and prove some fundamental properties of them. Further more by means of statistical e-convergence, we prove a Korovkin-type approximation theorem for double sequences of positive linear operators defined on the space of all 2 π-periodic and real valued-continuous functions on the real two-dimensional space.