On variations on quasi Cauchy sequences in metric spaces
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
For a fixed positive i nteger p, a sequence (xn) in a metric space X is c alled p-quasi-Cauchy if (?p xn) is a null sequence where ?p xn = d(xn+p, xn) for each positive integer n. A subset E of X is called p-ward compact if any sequence (xn) 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(xn)) is a p-quasi Cauchy sequence in Y whenever (xn) 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(xn) is p-quasi Cauchy in Y whenever (xn) is a quasi cauchy sequence of points in E.
Açıklama
Anahtar Kelimeler
Sequences, Series, Summability, Compactness, Continuity
Kaynak
International Conference of Mathematical Sciences
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
Sayı
Künye
İnce Dağcı, F., Çakallı, H. (2019). On variations on quasi Cauchy sequences in metric spaces. International Conference of Mathematical Sciences. s. 030012(1)-030012(3).
