Some further results on ideal summability of nets in (Formula Presented.) groups
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Birkhauser Verlag AG
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper we continue in the line of recent investigation of order summability of nets using ideals by Boccuto et al. (Czechoslovak Math. J. 62(137):1073–1083 2012; J. Appl. Anal. 20(1), 2014) where they had introduced the notions of I and (Formula Presented.) order convergence, I and (Formula Presented.) divergence of nets and its further extensions, namely the notions of (Formula Presented.)-order convergence and (Formula Presented.)-divergence of nets in a (Formula Presented.)-group and investigate the relation between (Formula Presented.)-concepts where a special class of ideals called (Formula Presented.)-ideals plays very important role. We also introduce, for the first time, the notion of (Formula Presented.)-order Cauchy condition and (Formula Presented.)-order cluster points of nets in ((Formula Presented.)) groups and examine some of its characterizations and its consequences. In particular the role of (Formula Presented.)-order cluster points in making the above mentioned Cauchy nets convergent is studied. © 2014, Springer Basel.
Açıklama
Anahtar Kelimeler
(?)-group, Filter, I-divergence, I-order-cluster point, I-order-convergence/Cauchy condition, IK-divergence, IK-order-convergence/Cauchy condition, Ideal, Net
Kaynak
Positivity
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
19
Sayı
1
