Generalized Almost Convergence and Core Theorems of Double Sequences

الملخص EN

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 = ( x j k ) into F [ λ ,   μ ] -convergence.

We also define a F [ λ ,   μ ] -core of x = ( x j k ) and determine a Tauberian condition for core inclusions and core equivalence.