A new variation on statistically quasi Cauchy sequences
International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017, Thessaloniki, Yunanistan, 25 - 30 Eylül 2017, cilt.1978, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1978
- Doi Numarası: 10.1063/1.5043981
- Basıldığı Şehir: Thessaloniki
- Basıldığı Ülke: Yunanistan
- Anahtar Kelimeler: continuity, quasi-Cauchy sequences, Statistical convergence
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (αk) of real numbers is called λ-statistically upward quasi-Cauchy if for every ϵ > 0 limn→∞1λn| {kΕIn:αk-αk+1≥ϵ} |=0, where (λn) is a non-decreasing sequence of positive numbers tending to ∞ such that λn+1 ≤ λn+1, λ1=1, and In=[n - λn+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. It turns out that the set of λ-statistical upward continuous is a proper subset of the set of uniformly continuous functions.