Ideal statistically quasi Cauchy sequences
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
AMER INST PHYSICS
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
An ideal I is a family of subsets of N, the set of positive integers which is closed under taking finite unions and subsets of its elements. A sequence (x(k)) of real numbers is said to be S(I)-statistically convergent to a real number L, if for each epsilon > 0 and for each delta > 0 the set {n is an element of N: 1/n {k <= n: vertical bar x(k) - L vertical bar >= epsilon}vertical bar >= delta} belongs to I. We introduce S(I)-statistically ward compactness of a subset of R, the set of real numbers, and S(I)-statistically ward continuity of a real function in the senses that a subset E of R is S(I)-statistically ward compact if any sequence of points in E has an S(I)-statistically quasi Cauchy subsequence, and a real function is S(I)-statistically ward continuous if it preserves S(I)-statistically quasi-Cauchy sequences where a sequence (x(k)) is called to be S(I)-statistically quasi-Cauchy when (Delta x(k)) is S(I)-statistically convergent to 0. We obtain results related to S(I)-statistically ward continuity, S(I)-statistically ward compactness, N-theta-ward continuity, and slowly oscillating continuity.
Açıklama
3rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTAN
Anahtar Kelimeler
Sequences, Ideal convergence, Compactness, Continuity
Kaynak
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016)
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
1759
