A Variation on Statistical Ward Continuity
Bulletin of the Malaysian Mathematical Sciences Society, cilt.40, sa.4, ss.1701-1710, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 40 Sayı: 4
- Basım Tarihi: 2017
- Doi Numarası: 10.1007/s40840-015-0195-0
- Dergi Adı: Bulletin of the Malaysian Mathematical Sciences Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1701-1710
- Anahtar Kelimeler: Boundedness, Quasi-Cauchy sequences, Statistical convergent sequences, Summability, Uniform continuity
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (αk) of points in R, the set of real numbers, is called ρ-statistically convergent to an element ℓ of R if (Formula presented.) for each ε> 0 , where ρ= (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim supnρnn<∞, Δ ρn= O(1) , and Δ αn= αn + 1- αn for each positive integer n. A real-valued function defined on a subset of R is called ρ-statistically ward continuous if it preserves ρ-statistical quasi-Cauchy sequences where a sequence (αk) is defined to be ρ-statistically quasi-Cauchy if the sequence (Δ αk) is ρ-statistically convergent to 0. We obtain results related to ρ-statistical ward continuity, ρ-statistical ward compactness, ward continuity, continuity, and uniform continuity. It turns out that the set of uniformly continuous functions coincides with the set of ρ-statistically ward continuous functions not only on a bounded subset of R, but also on an interval.