Generalized Almost Convergence and Core Theorems of Double Sequences

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 onF[λ, μ]such that it is a Banach space and then we define and characterize those four-dimensional matrices which transformF[λ, μ]-convergence of double sequencesx=(xjk)intoF[λ, μ]-convergence. We also define aF[λ, μ]-core ofx=(xjk)and determine a Tauberian condition for core inclusions and core equivalence.