Statistical cluster points of sequences in finite dimensional spaces
CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.54, sa.1, ss.95-102, 2004 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 54 Sayı: 1
- Basım Tarihi: 2004
- Doi Numarası: 10.1023/b:cmaj.0000027250.19041.72
- Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.95-102
- Süleyman Demirel Üniversitesi Adresli: Hayır
Özet
In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of Gamma-statistical convergence. A sequence x is Gamma-statistically convergent to a set C if C is a minimal closed set such that for every epsilon > 0 the set {k: rho(C, x(k)) greater than or equal to epsilon} has density zero. It is shown that every statistically bounded sequence is Gamma-statistically convergent. Moreover if a sequence is Gamma-statistically convergent then the limit set is a set of statistical cluster points.