Ideal statistically quasi Cauchy sequences
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Institute of Physics Inc.
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 (xk) of real numbers is said to be S(I)-statistically convergent to a real number L, if for each ? > 0 and for each ? > 0 the set { n?N:1n| { k?n:| xk-L |?? } |?? } 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 (xk) is called to be S(I)-statistically quasi-Cauchy when (?xk) is S(I)-statistically convergent to 0. We obtain results related to S(I)-statistically ward continuity, S(I)-statistically ward compactness, N?-ward continuity, and slowly oscillating continuity. © 2016 Author(s).
Açıklama
3rd International Conference on Analysis and Applied Mathematics, ICAAM 2016 -- 7 September 2016 through 10 September 2016 -- -- 123415
Anahtar Kelimeler
Compactness, Continuity, Ideal convergence, Sequences
Kaynak
AIP Conference Proceedings
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
1759
