Statistical cluster points of sequences in finite dimensional spaces

Pehlivan, Serpil, Güncan, A., and Mamedov, M. A.. "Statistical cluster points of sequences in finite dimensional spaces." Czechoslovak Mathematical Journal 54.1 (2004): 95-102. <http://eudml.org/doc/30840>.

@article{Pehlivan2004,
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 $ \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.},
author = {Pehlivan, Serpil, Güncan, A., Mamedov, M. A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {compact sets; natural density; statistically bounded sequence; statistical cluster point; compact set; natural density; statistically bounded sequence; statistical cluster point},
language = {eng},
number = {1},
pages = {95-102},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Statistical cluster points of sequences in finite dimensional spaces},
url = {http://eudml.org/doc/30840},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Pehlivan, Serpil
AU - Güncan, A.
AU - Mamedov, M. A.
TI - Statistical cluster points of sequences in finite dimensional spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 95
EP - 102
AB - 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.
LA - eng
KW - compact sets; natural density; statistically bounded sequence; statistical cluster point; compact set; natural density; statistically bounded sequence; statistical cluster point
UR - http://eudml.org/doc/30840
ER -