On λ statistical upward compactness and continuity
Filomat, cilt.32, sa.12, ss.4435-4443, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 32 Sayı: 12
- Basım Tarihi: 2018
- Doi Numarası: 10.2298/fil1812435c
- Dergi Adı: Filomat
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.4435-4443
- Anahtar Kelimeler: Continuity, Quasi-Cauchy sequences, Sequences, Statistical convergence
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (α k ) of real numbers is called λ-statistically upward quasi-Cauchy if for every (forumala presented)., where (λ n ) is a non-decreasing sequence of positive numbers tending to ∞ such n that λ n+1 ≤ λ n + 1, λ 1 = 1, and I n = [n − λ n + 1, n] for any positive integer n. A real valued function f defined on a subset of R, the set of real numbers is λ-statistically upward continuous if it preserves λ-statistical upward quasi-Cauchy sequences. λ-statistically upward compactness of a subset in real numbers is also introduced and some properties of functions preserving such quasi Cauchy sequences are investigated. It turns out that a function is uniformly continuous if it is λ-statistical upward continuous on a λ-statistical upward compact subset of ℝ.