Statistical ward continuity
Applied Mathematics Letters, cilt.24, sa.10, ss.1724-1728, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24 Sayı: 10
- Basım Tarihi: 2011
- Doi Numarası: 10.1016/j.aml.2011.04.029
- Dergi Adı: Applied Mathematics Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1724-1728
- Anahtar Kelimeler: Boundedness, Quasi-Cauchy sequences, Statistical convergent sequences, Summability, Uniform continuity
- Maltepe Üniversitesi Adresli: Evet
Özet
Recently, it has been proved that a real-valued function defined on an interval A of R, the set of real numbers, is uniformly continuous on A if and only if it is defined on A and preserves quasi-Cauchy sequences of points in A. In this paper we call a real-valued function statistically ward continuous if it preserves statistical quasi-Cauchy sequences where a sequence (αk) is defined to be statistically quasi-Cauchy if the sequence (Δαk) is statistically convergent to 0. It turns out that any statistically ward continuous function on a statistically ward compact subset A of R is uniformly continuous on A. We prove theorems related to statistical ward compactness, statistical compactness, continuity, statistical continuity, ward continuity, and uniform continuity. © 2011 Elsevier Ltd. All rights reserved.