1. Statistical cluster points of sequences in finite dimensional spaces
- Creator:
- Pehlivan;, Serpil, Güncan, A., and Mamedov, M. A.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- compact sets, natural density, statistically bounded sequence, and statistical cluster point
- Language:
- English
- Description:
- 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 $ \lbrace k\:\rho (C, x_k ) \ge \epsilon \rbrace $ 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public