On variations of quasi-Cauchy sequences in cone metric spaces
Filomat, cilt.30, sa.3, ss.603-610, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 30 Sayı: 3
- Basım Tarihi: 2016
- Doi Numarası: 10.2298/fil1603603c
- Dergi Adı: Filomat
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.603-610
- Anahtar Kelimeler: Cone metric, Continuity, Convergence, Metric spaces, Metrizability, Summability, Total boundedness
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (xn) of points in a topological vector space valued cone metric space (X;ρ) is called p-quasi-Cauchy if for each c Є K there exists an n0 Є ℕ such that ρ(xn+p, xn) - c Є K for n ≥ n0, where K is a proper, closed and convex pointed cone in a topological vector space γ with K ≠ θ. We investigate p-ward continuity in topological vector space valued cone metric spaces. It turns out that p-ward continuity coincides with uniform continuity not only on a totally bounded subset but also on a connected subset of X.