Statistical quasi Cauchyness on asymmetric spaces

Dagci F. I.

Filomat, cilt.39, sa.18, ss.6383-6390, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 18
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2518383d
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.6383-6390
  • Anahtar Kelimeler: asymmetric metric, compactness, continuity
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

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.