Statistical Cluster Points of Sequences in Finite Dimensional Spaces
By Serpil Pehlivan, A. Güncan, M. A. Mamedov. 2004
53 citations recorded by the source corpus.
AbstractIn 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.
Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b583aff516ea8959f91e7d90b8b94f24f01ec938
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In Management Science and Operations Research
In Numerical Analysis
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Citations in the corpus
- On Ideal Convergent Sequences in 2-Normed Spaces (2006, background): “Since then, this concept has been studied by many authors, see for instance [3, 10].”
- ON I-CAUCHY SEQUENCES (2007, background): “The concept of statistical convergence was introduced by Steinhaus [21] in 1951 (see also Fast [5]) and has been discussed and developed by many authors including [2, 4, 7-9, 15-18, 20].”
- Rough Statistical Convergence (2008, background): “We briefly recall some of the basic notions in the theory of statistical convergence, and we refer readers to [3, 4, 6, 8, 13] for more details.”