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.
Highlights
The idea of [λ, μ]-almost 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 we define and characterize those four-dimensional matrices which transform F[λ,μ]-convergence of double sequences x = into F[λ,μ]-convergence
We begin by recalling the definition of convergence for double sequences which was introduced by Pringsheim [1]
Summary
A double sequence x = (xjk) is said to be conVergent to L in the Pringsheim’s sense (or P-convergent to L) if for given ε > 0 there exists an integer N such that |xjk − L| < ε whenever j, k > N. We denote by CBP the space of all boundedly P-convergent double sequences. A sequence x = (xj) in l∞ is almost convergent to L if all of its Banach limits are equal, where l∞ denotes the space of all bounded sequences.
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