Statistical quasi Cauchyness on asymmetric spaces

Dagci F. I.

Filomat, vol.39, no.18, pp.6383-6390, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 18
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2518383d
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6383-6390
  • Keywords: asymmetric metric, compactness, continuity
  • Istanbul Kültür University Affiliated: Yes

Abstract

We call a sequence (xm) of points in an asymmetric metric space (X, d) statistically forward quasi 1 Cauchy if lim (Formula present) for each positive ε, where |A| indicates the cardinality of the set A. We prove that a subset E of X is forward totally bounded if and only if any sequence of points in E has a statistically forward quasi Cauchy subsequence. We also introduce and investigate statistically upward continuity in the sense that a function defined on X into Y is called statistically upward continuous if it preserves statistically forward quasi Cauchy sequences, i.e. (f (xm)) is statistically forward quasi Cauchy whenever (xm) is.