Variations on ward continuity in 2-normed spaces


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Ersan S. S.

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: 10.1063/1.5136142
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: 2-normed space, compactness, continuity, Sequences, series, summability
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Maltepe Üniversitesi Adresli: Evet

Özet

In this paper, the concept of a quasi-Cauchy sequence is generalized to a concept of a p-quasi-Cauchy sequence for any fixed positive integer p in a 2-normed space X. Some interesting theorems related to p-ward continuity and uniform continuity are obtained. A sequence (xn) in a 2-normed space X is called p-quasi-Cauchy if limn→∞-xn+p-xn, z-= 0 for all z ℓ X. It turns out that if a function f defined on a subset of X is uniformly continuous, then f preserves p-quasi-Cauchy sequences for all positive integer p.