On variations on quasi Cauchy sequences in metric spaces
International Conference of Mathematical Sciences 2018, ICMS 2018, İstanbul, Türkiye, 31 Temmuz - 06 Ağustos 2018, cilt.2086, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 2086
- Doi Numarası: 10.1063/1.5095097
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: compactness, continuity, Sequences, series, summability
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Maltepe Üniversitesi Adresli: Evet
Özet
For a fixed positive i nteger p, a sequence (x n ) in a metric space X is c alled p-quasi-Cauchy if (Δ p x n ) is a null sequence where Δ p x n =d(x n+p , x n ) for each positive integer n. A subset E of X is called p-ward compact if any sequence (x n ) of points in E has a p-quasi-Cauchy subsequence. A subset of X is totally bounded if and only if it is p-ward compact. A function f from a subset E of X into a metric space Y is called p-ward continuous if it preserves p-quasi Cauchy sequences, i.e. (f (x n )) is a p-quasi Cauchy sequence in Y whenever (x n ) is a p-quasi Cauchy sequence of points of E. A function f from a totally bounded subset of X into Y preserves p-quasi Cauchy sequences if and only if it is uniformly continuous. If a function is uniformly continuous on a subset E of X into Y, then (f (x n ) is p-quasi Cauchy in Y whenever (x n ) is a quasi cauchy sequence of points in E.