Abstract and Applied Analysis

Generalized Almost Convergence and Core Theorems of Double Sequences

S. A. Mohiuddine and Abdullah Alotaibi

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Abstract

The idea of [ λ ,   μ ] -almost convergence (briefly, F [ λ ,   μ ] -convergence) has been recently introduced and studied by Mohiuddine and Alotaibi (2014). In this paper first we define a norm on F [ λ ,   μ ] such that it is a Banach space and then we define and characterize those four-dimensional matrices which transform F [ λ ,   μ ] -convergence of double sequences x = ( x j k ) into F [ λ ,   μ ] -convergence. We also define a F [ λ ,   μ ] -core of x = ( x j k ) 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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