Statistical Cluster Points of Sequences in Finite Dimensional Spaces |
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Authors: | S Pehlivan A Güncan M A Mamedov |
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Institution: | (1) Dept of Mathematics, Süleyman Demirel University, Cunur Campus, 32260 Isparta, Turkey;(2) School of ITMS, University of Ballarat, 3353 Vic, Australia |
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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 -statistical convergence. A sequence xis -statistically convergent to a set Cif Cis a minimal closed set such that for every > 0 the set
has density zero. It is shown that every statistically bounded sequence is -statistically convergent. Moreover if a sequence is -statistically convergent then the limit set is a set of statistical cluster points. |
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Keywords: | compact sets natural density statistically bounded sequence statistical cluster point |
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