Two valued measure and summability of double sequences

Das, Pratulananda, and Bhunia, Santanu. "Two valued measure and summability of double sequences." Czechoslovak Mathematical Journal 59.4 (2009): 1141-1155. <http://eudml.org/doc/37984>.

@article{Das2009,
abstract = {In this paper, following the methods of Connor [connor], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [moe]) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor [jc]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$).},
author = {Das, Pratulananda, Bhunia, Santanu},
journal = {Czechoslovak Mathematical Journal},
keywords = {double sequences; $\mu $-statistical convergence; divergence and Cauchy criteria; convergence; divergence and Cauchy criteria in $\mu $-density; condition (APO$_2)$; double sequence; -statistical convergence; divergence criteria; Cauchy criteria; convergence; -density; condition (APO},
language = {eng},
number = {4},
pages = {1141-1155},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two valued measure and summability of double sequences},
url = {http://eudml.org/doc/37984},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Das, Pratulananda
AU - Bhunia, Santanu
TI - Two valued measure and summability of double sequences
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 1141
EP - 1155
AB - In this paper, following the methods of Connor [connor], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [moe]) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor [jc]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$).
LA - eng
KW - double sequences; $\mu $-statistical convergence; divergence and Cauchy criteria; convergence; divergence and Cauchy criteria in $\mu $-density; condition (APO$_2)$; double sequence; -statistical convergence; divergence criteria; Cauchy criteria; convergence; -density; condition (APO
UR - http://eudml.org/doc/37984
ER -