Two valued measure and summability of double sequences

Title:

Two valued measure and summability of double sequences

Creator:

Das, Pratulananda and Bhunia, Santanu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:43babd54-f524-4320-92c5-bab60dc367c0
uuid:43babd54-f524-4320-92c5-bab60dc367c0

Subject:

double sequences, $\mu $-statistical convergence, divergence and Cauchy criteria, convergence, divergence and Cauchy criteria in $\mu $-density, and condition (APO$_2)$

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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$_2$).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1141-1155

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:4

Harvested from:

CDK

Metadata only:

false