Statistical cluster points of sequences in finite dimensional spaces


Pehlivan S., Guncan A., Mamedov M.

CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.54, ss.95-102, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 54 Konu: 1
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:cmaj.0000027250.19041.72
  • Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.95-102

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.