Upward and Downward Statistical Continuities
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
UNIV NIS, FAC SCI MATH
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A real valued function f defined on a subset E of R, the set of real numbers, is statistically upward (resp. downward) continuous if it preserves statistically upward (resp. downward) half quasi-Cauchy sequences; A subset E of R, is statistically upward (resp. downward) compact if any sequence of points in E has a statistically upward (resp. downward) half quasi-Cauchy subsequence, where a sequence (x(n)) of points in R is called statistically upward half quasi-Cauchy if lim(n ->infinity) 1/n vertical bar{k <= n : x(k) - x(k+1) >= epsilon}vertical bar = 0 and statistically downward half quasi-Cauchy if lim(n ->infinity) 1/n vertical bar{k <= n : x(k+1) - x(k) >= epsilon}vertical bar = 0 for every epsilon > 0. We investigate statistically upward and downward continuity, statistically upward and downward half compactness and prove interesting theorems. It turns out that any statistically upward continuous function on a below bounded subset of R is uniformly continuous, and any statistically downward continuous function on an above bounded subset of R is uniformly continuous.
Açıklama
Anahtar Kelimeler
continuity, compactness, sequences, summability
Kaynak
FILOMAT
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
29
Sayı
10
