Delta Quasi Cauchy Sequences in Metric Spaces


Cakalli H.

4th International Conference of Mathematical Sciences, ICMS 2020, İstanbul, Türkiye, 17 - 21 Haziran 2020, cilt.2334, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2334
  • Doi Numarası: 10.1063/5.0042190
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: Compactness, Continuity, Metric spaces, Sequences
  • Maltepe Üniversitesi Adresli: Evet

Özet

In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cauchy if limn!1[d(xk+2; xk+1)d(xk+1; xk)] = 0. A new type compactness in terms of δ-quasi Cauchy sequences, namely δ ward compactness is also introduced, and some theorems related to δ-ward continuity and δ-ward compactness are obtained. Some other types of continuities are also discussed, and interesting results are obtained.