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Statistical Cluster Points of Sequences in Finite Dimensional Spaces

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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 Γ-statistical convergence. A sequence xis Γ-statistically convergent to a set Cif Cis a minimal closed set such that for every ∈ > 0 the set \(\{ k:\varrho (C,x_{{\text{ }}k} ) \geqslant \varepsilon \} \)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.

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Authors and Affiliations

  1. Dept of Mathematics, Süleyman Demirel University, Cunur Campus, 32260, Isparta, Turkey

    S. Pehlivan & A. Güncan

  2. School of ITMS, University of Ballarat, 3353, Vic, Australia

    M. A. Mamedov

Authors
  1. S. Pehlivan
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  2. A. Güncan
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  3. M. A. Mamedov
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Pehlivan, S., Güncan, A. & Mamedov, M.A. Statistical Cluster Points of Sequences in Finite Dimensional Spaces. Czechoslovak Mathematical Journal 54, 95–102 (2004). https://doi.org/10.1023/B:CMAJ.0000027250.19041.72

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  • DOI: https://doi.org/10.1023/B:CMAJ.0000027250.19041.72

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