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Abstract and Applied Analysis
Volume 2014, Article ID 152910, 7 pages
Research Article

Generalized Almost Convergence and Core Theorems of Double Sequences

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 15 May 2014; Accepted 15 June 2014; Published 15 July 2014

Academic Editor: Abdul Latif

Copyright © 2014 S. A. Mohiuddine and Abdullah Alotaibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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