LACUNARY STATISTICALLY UPWARD AND DOWNWARD HALF QUASI-CAUCHY SEQUENCES
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
UNIV PRISHTINES
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (x(k)) of points in R is called lacunary statistically upward half quasi Cauchy if lim(r infinity) 1/h(r) vertical bar{k is an element of I-r : x(k) - x(k+1) >= epsilon}vertical bar - 0 for every epsilon > 0; and (x(k)) is called lacunary statistically downward half quasi-Cauchy if lim(r ->infinity) 1/h(r) vertical bar {k is an element of I-r : x(k+1) - x(k) >= epsilon}vertical bar = 0 for every epsilon > 0, where theta = (k(r)) is an increasing sequence of non-negative integers such that k(0) = 1 and h(r) : k(r) - k(r-1) -> infinity. We investigate lacunary statistically upward continuity and lacunary statistically downward continuity and prove some interesting theorems. It turns out that not only a lacunary statistically upward continuous function on a below bounded subset, but also a lacunary statistically downward continuous function on an above bounded subset is uniformly continuous.
Açıklama
Anahtar Kelimeler
Summability, lacunary statistical convergence, boundedness and continuity
Kaynak
JOURNAL OF MATHEMATICAL ANALYSIS
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
7
Sayı
2
