Geodesic
Two valued measure and summability of double sequences
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1141-1155

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper, following the methods of Connor \cite {connor}, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely \cite {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 \cite {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$_2$).
Classification : 40A05, 40A30, 40B05
Keywords: double sequences; $\mu $-statistical convergence; divergence and Cauchy criteria; convergence; divergence and Cauchy criteria in $\mu $-density; condition (APO$_2)$ 
@article{CMJ_2009__59_4_a21,
     author = {Das, Pratulananda and Bhunia, Santanu},
     title = {Two valued measure and summability of double sequences},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1141--1155},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {2009},
     mrnumber = {2563584},
     zbl = {1224.40009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a21/}
}
TY  - JOUR
AU  - Das, Pratulananda
AU  - Bhunia, Santanu
TI  - Two valued measure and summability of double sequences
JO  - Czechoslovak Mathematical Journal
PY  - 2009
SP  - 1141
EP  - 1155
VL  - 59
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a21/
LA  - en
ID  - CMJ_2009__59_4_a21
ER  - 
%0 Journal Article
%A Das, Pratulananda
%A Bhunia, Santanu
%T Two valued measure and summability of double sequences
%J Czechoslovak Mathematical Journal
%D 2009
%P 1141-1155
%V 59
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a21/
%G en
%F CMJ_2009__59_4_a21
Das, Pratulananda; Bhunia, Santanu. Two valued measure and summability of double sequences. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1141-1155. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a21/