Statistical cluster points of sequences in finite dimensional spaces

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PEHLİVAN S., Güngan A., MƏMMƏDOV M.

Czechoslovak Mathematical Journal, vol.54, no.1, pp.95-102, 2004 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 54 Say: 1
  • Nəşr tarixi: 2004
  • Doi nömrəsi: 10.1023/b:cmaj.0000027250.19041.72
  • jurnalın adı: Czechoslovak Mathematical Journal
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.95-102
  • Açar sözlər: Compact sets, Natural density, Statistical cluster point, Statistically bounded sequence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

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 T-statistical convergence. A sequence x is Γ-statistically convergent to a set C if C is a minimal closed set such that for every ε 0 the set {k: ρ(C,xk) ≥ ε} has density zero. It is shown that every statistically bounded sequence is Γ-statistically convergent. Moreover if a sequence is Γ-statistically convergent then the limit set is a set of statistical cluster points.