Generalized Almost Convergence and Core Theorems of Double Sequences - S. A. Mohiuddine; Abdullah Alotaibi (Abstract and Applied Analysis)
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=(xjk) into F[λ, μ]-convergence. We also define a F[λ, μ]-core of x=(xjk) and determine a Tauberian condition for core inclusions and core equivalence.