On statistically convergent sequences of closed sets

Talo Ö., Sever Y., Başar F.

Filomat, vol.30, no.6, pp.1497-1509, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1606497t
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1497-1509
  • Keywords: Kuratowski statistical convergence, Sequence of sets, Statistical convergence, Statistical inner limit, Statistical outer limit
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, we give the definitions of statistical inner and outer limits for sequences of closed sets in metric spaces. We investigate some properties of statistical inner and outer limits. For sequences of closed sets if its statistical outer and statistical inner limits coincide, we say that the sequence is Kuratowski statistically convergent. We prove some proporties for Kuratowski statistically convergent sequences. Also, we examine the relationship between Kuratowski statistical convergence and Hausdorff statistical convergence.