Beyond Cauchy and Quasi-Cauchy Sequences
Küçük Resim Yok
Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
UNIV NIS, FAC SCI MATH
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we investigate the concepts of downward continuity and upward continuity. A real valued function on a subset E of R, the set of real numbers, is downward continuous if it preserves downward quasi-Cauchy sequences; and is upward continuous if it preserves upward quasi-Cauchy sequences, where a sequence (x(k)) of points in R is called downward quasi-Cauchy if for every epsilon > 0 there exists an n(0) is an element of N such that x(n+1) xn < epsilon for n >= n(0), and called upward quasi-Cauchy if for every epsilon > 0 there exists an n(1) is an element of N such that xn x(n+1) < epsilon for n >= n(1). We investigate the notions of downward compactness and upward compactness and prove that downward compactness coincides with above boundedness. It turns out that not only the set of downward continuous functions, but also the set of upward continuous functions is a proper subset of the set of continuous functions.
Açıklama
3rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTAN
Anahtar Kelimeler
Sequences, series, summability, continuity
Kaynak
FILOMAT
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
32
Sayı
3
