Rho statistical convergence of order beta
3rd International Conference of Mathematical Sciences, ICMS 2019, İstanbul, Türkiye, 4 - 08 Eylül 2019, cilt.2183, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 2183
- Doi Numarası: 10.1063/1.5136141
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Anahtar Kelimeler: functional analysis, Sequences, series, summability
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Maltepe Üniversitesi Adresli: Evet
Özet
A sequence (αk) of points in R, the set of real numbers, is called ρ-statistically convergent of order β to an element R of R if limn→∞Rρnβ| { k≤n:| αk-R |≥ϵ |=0 for each ϵ > 0 and 0 < β ≤ 1, where ρ = (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim supnρnβn<∞, Δρnβ=O(1), and Δαn = 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 (Δαk) is ρ-statistically convergent to 0. We obtain results related to ρ-statistical ward continuity of order β, ρ-statistical ward compactness of order β, ward continuity, continuity, and uniform continuity.