Statistically D-bounded sequences in probabilistic normed spaces

Sencimen C., Pehlivan S.

APPLICABLE ANALYSIS, vol.88, no.8, pp.1133-1142, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 88 Issue: 8
  • Publication Date: 2009
  • Doi Number: 10.1080/00036810903114742
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1133-1142


In this study, the concept of a statistically D-bounded sequence in a probabilistic normed (PN) space endowed with the strong topology is introduced and its basic properties are investigated. It is shown that a strongly statistically convergent sequence and a strong statistically Cauchy sequence are statistically D-bounded under certain conditions. A sequence which goes far away from the limit point infinitely many times and presents random deviations in a PN space may be handled with the tools of strong statistical convergence and statistical D-boundedness.