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 (SCI-Expanded) identifier identifier

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.