Statistically quasi Cauchy sequences in abstract metric spaces

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Sonmez A., Cakalli H.

3rd International Conference of Mathematical Sciences, ICMS 2019, İstanbul, Türkiye, 4 - 08 Eylül 2019, cilt.2183, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2183
  • Doi Numarası: 10.1063/1.5136136
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: compactness, cone metric, continuity, Sequences, series
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Maltepe Üniversitesi Adresli: Evet

Özet

In this extended abstract, we introduce a concept of statistically quasi-Cauchyness of a sequence in X in the sense that a sequence (xk) is statistically quasi-Cauchy in X if limn→∞ 1n |{k ≤ n: d(xk+1, xk)-c ℓ P}| for each c ℓP where (X, d) is a cone metric space, and P denotes interior of a cone P of X. It turns out that a function f from a totally bounded subset A of X into X is uniformly continuous if f preserves statistically quasi-Cauchy sequences.