Variations on Rho statistical quasi Cauchy sequences
International Conference of Mathematical Sciences 2018, ICMS 2018, İstanbul, Türkiye, 31 Temmuz - 06 Ağustos 2018, cilt.2086, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 2086
- Doi Numarası: 10.1063/1.5095095
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: compactness, continuity., Sequences, series, summability
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (α k ) of points in R, the set of real numbers, is called ρ-statistically p quasi Cauchy if limn→81ρn|{k≤n:|Δpαk|≥ϵ}|=0 for each ϵ > 0, where ρ = (ρ n ) is a non-decreasing sequence of positive real numbers tending to 8 such that lim supnρnn<8, Δρ n = O(1) and Δ p α k+p = α k+p - α k for each positive integer k, p is a fixed positive integer. A real-valued function defined on a subset of R is called ρ-statistically p-ward continuous if it preserves ρ-statistical p-quasi Cauchy sequences. We obtain results related to ρ-statistical p-ward continuity, ρ-statistical p-ward compactness, p-ward continuity, ward continuity, and uniform continuity.