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