Generalized Almost Convergence and Core Theorems of Double Sequences

S. A. Mohiuddine and Abdullah Alotaibi

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 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.

Date: 2014
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https://doi.org/10.1155/2014/152910

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:152910

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