Beyond the quasi-Cauchy sequences beyond the Cauchy sequences
3rd International Conference on Analysis and Applied Mathematics, ICAAM 2016, Almaty, Kazakistan, 7 - 10 Eylül 2016, cilt.1759, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1759
- Doi Numarası: 10.1063/1.4959626
- Basıldığı Şehir: Almaty
- Basıldığı Ülke: Kazakistan
- Anahtar Kelimeler: Continuity, Sequences, Series, Summability
- Maltepe Üniversitesi Adresli: Evet
Özet
In this paper, we investigate the concept of upward continuity. A real valued function on a subset E of R, the set of real numbers is upward continuous if it preserves upward quasi Cauchy sequences in E, where a sequence (xk) of points in R is called upward quasi Cauchy if for every ϵ > 0 there exists a positive integer n0 such that xn - xn+1 < ϵ for n ≥ n0. It turns out that the set of upward continuous functions is a proper subset of the set of continuous functions.