Forward continuity
Journal of Computational Analysis and Applications, cilt.13, sa.2, ss.225-230, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 13 Sayı: 2
- Basım Tarihi: 2011
- Dergi Adı: Journal of Computational Analysis and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.225-230
- Anahtar Kelimeler: Compactness, Continuity, Sequences, Series, Summability
- Maltepe Üniversitesi Adresli: Evet
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→∞ Δf(xn) = 0 whenever limn→∞ Δxn = 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→∞ Δzk = 0 where Δzk = zk+1-zk. We investigate forward continuity and forward compactness, and prove related theorems. © 2011 by Eudoxus Press,LLC All rights reserved.