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.
S. A. Mohiuddine. Abdullah Alotaibi. "Generalized Almost Convergence and Core Theorems of Double Sequences." Abstr. Appl. Anal. 2014 (SI71) 1 - 7, 2014. https://doi.org/10.1155/2014/152910