## Abstract and Applied Analysis

### Generalized Almost Convergence and Core Theorems of Double Sequences

#### Abstract

The idea of $[\lambda , \mu ]$-almost convergence (briefly, ${\mathcal{F}}_{[\lambda , \mu ]}$-convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm on ${\mathcal{F}}_{[\lambda , \mu ]}$ such that it is a Banach space and then we define and characterize those four-dimensional matrices which transform ${\mathcal{F}}_{[\lambda , \mu ]}$-convergence of double sequences $x=({x}_{jk})$ into ${\mathcal{F}}_{[\lambda , \mu ]}$-convergence. We also define a ${\mathcal{F}}_{[\lambda , \mu ]}$-core of $x=({x}_{jk})$ and determine a Tauberian condition for core inclusions and core equivalence.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 152910, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606009

Digital Object Identifier
doi:10.1155/2014/152910

Mathematical Reviews number (MathSciNet)
MR3240525

Zentralblatt MATH identifier
07021818

#### Citation

Mohiuddine, S. A.; Alotaibi, Abdullah. Generalized Almost Convergence and Core Theorems of Double Sequences. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 152910, 7 pages. doi:10.1155/2014/152910. https://projecteuclid.org/euclid.aaa/1412606009

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