Forward continuity
Küçük Resim Yok
Tarih
2011
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A real function f is continuous if and only if (f(xn)) is a convergent sequence whenever (xn) is convergent and a subset E of R is compact if any sequence x = (xn) of points in E has a convergent subsequence whose limit is in E where R is the set of real numbers. These well known results suggest us to introduce a concept of forward continuity in the sense that a function f is forward continuous if limn›? ?f(xn) = 0 whenever limn›? ?xn = 0 and a concept of forward compactness in the sense that a subset E of R is forward compact if any sequence x = (xn) of points in E has a subsequence z = (zk) = (xnk) of the sequence x such that limk›? ?zk = 0 where ?zk = zk+1-zk. We investigate forward continuity and forward compactness, and prove related theorems. © 2011 by Eudoxus Press,LLC All rights reserved.
Açıklama
Anahtar Kelimeler
Compactness, Continuity, Sequences, Series, Summability
Kaynak
Journal of Computational Analysis and Applications
WoS Q Değeri
Scopus Q Değeri
Q4
Cilt
13
Sayı
2
