A variation on lacunary quasi Cauchy sequences
[ X ]
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Physics
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order alpha of real numbers in the sense that a sequence (x(k)) of points in R is called I lacunary statistically quasi-Cauchy of order alpha, if {r is an element of N : 1/h(r)(a) vertical bar Delta x(k)vertical bar >= epsilon vertical bar >= epsilon vertical bar >= delta}is an element of I for each epsilon > 0 and for each delta > 0, where an ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. The main purpose of this paper is to investigate ideal lacunary statistical ward continuity of order alpha, where a function f is called I lacunary statistically ward continuous of order alpha if it preserves I-lacunary statistically quasi-Cauchy sequences of order alpha, i.e. (f(x(n))) is a s(theta)(alpha)(I)-quasi-Cauchy sequence whenever (x(n)) is.
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
Q4
Cilt
1759
