Variations on statistical quasi Cauchy sequences
Boletim da Sociedade Paranaense de Matematica, cilt.38, sa.3, ss.141-150, 2020 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 3
- Basım Tarihi: 2020
- Doi Numarası: 10.5269/bspm.v38i3.39991
- Dergi Adı: Boletim da Sociedade Paranaense de Matematica
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
- Sayfa Sayıları: ss.141-150
- Anahtar Kelimeler: Compactness, Continuity, Real functions, Sequences, Series
- Maltepe Üniversitesi Adresli: Evet
Özet
In this paper, we introduce a concept of statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (α k ) is statistically p-quasi-Cauchy if limn→∞ n 1 |{k ≤ n: |αk+ p − α k | ≥ ε}| = 0 for each ε > 0. A function f is called statistically p-ward continuous on a subset A of the set of real umbers R if it preserves statistically p-quasi-Cauchy sequences, i.e. the sequence f(x) = (f(αn)) is statistically p-quasi-Cauchy whenever α = (αn) is a statistically p-quasi-Cauchy sequence of points in A. It turns out that a real valued function f is uniformly continuous on a bounded subset A of R if there exists a positive integer p such that f preserves statistically p-quasi-Cauchy sequences of points in A.