N-theta-Ward Continuity
Küçük Resim Yok
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
HINDAWI LTD
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
A function f is continuous if and only if f preserves convergent sequences; that is, (f(alpha(n))) is a convergent sequence whenever (alpha(n)) is convergent. The concept of N-theta-ward continuity is defined in the sense that a function f is N-theta-ward continuous if it preserves N-theta-quasi-Cauchy sequences; that is, (f(alpha(n))) is an N-theta-quasi-Cauchy sequence whenever (alpha(n)) is N-theta-quasi-Cauchy. A sequence (alpha(k)) of points in R, the set of real numbers, is N-theta-quasi-Cauchy if lim(r ->infinity) (1/h(r)) Sigma(k is an element of Ir) vertical bar Delta alpha(k)vertical bar = 0, where Delta alpha(k) = alpha(k+1) - alpha(k), I-r = (k(r-1), k(r)], and theta = (k(r)) is a lacunary sequence, that is, an increasing sequence of positive integers such that k(0) = 0 and h(r) : k(r) - k(r-1) -> infinity. A new type compactness, namely, N-theta-ward compactness, is also, defined and some new results related to this kind of compactness are obtained.
Açıklama
Anahtar Kelimeler
Kaynak
ABSTRACT AND APPLIED ANALYSIS
WoS Q Değeri
Q1
Scopus Q Değeri
Q4
