Variations on ward continuity in 2-normed spaces
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.