Upward and downward statistical continuities
Filomat, cilt.29, sa.10, ss.2265-2273, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 29 Sayı: 10
- Basım Tarihi: 2015
- Doi Numarası: 10.2298/fil1510265c
- Dergi Adı: Filomat
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.2265-2273
- Anahtar Kelimeler: Compactness, Continuity, Sequences, Summability
- Maltepe Üniversitesi Adresli: Evet
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 (xn) of points in R is called statistically upward half quasi-Cauchy if (formula presented) and statistically downward half quasi-Cauchy if (formula presented) for every ε > 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.