A CHARACTERIZATION THEOREM FOR LEVELWISE STATISTICAL CONVERGENCE


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Aytar S.

FILOMAT, vol.25, no.1, pp.133-143, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 1
  • Publication Date: 2011
  • Doi Number: 10.2298/fil1101133a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.133-143

Abstract

In the present paper, we prove a characterization theorem which gives a necessary and sufficient condition for a sequence of fuzzy numbers to be levelwise statistically convergent in the space of fuzzy numbers. As an application of this theorem we utilize the idea of statistical equi-continuity in order to obtain a condition which guarantees the set of levelwise statistical cluster points of a statistically bounded sequence to be nonempty and a levelwise statistically Cauchy sequence to be levelwise statistically convergent.