Statistical cluster points of sequences in finite dimensional spaces


Pehlivan S., Guncan A., Mamedov M.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.54, no.1, pp.95-102, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.1023/b:cmaj.0000027250.19041.72
  • Title of Journal : CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Page Numbers: pp.95-102

Abstract

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.