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Generalized almost convergence and core theorems of double sequences. (English) Zbl 1470.40006

Summary: The idea of \([\lambda, \mu]\)-almost convergence (briefly, \(\mathcal{F}_{[\lambda, \mu]}\)-convergence) has been recently introduced and studied by us [ibid. 2014, Article ID 412974, 6 p. (2014; Zbl 1469.40002)]. In this paper first we define a norm on \(\mathcal{F}_{[\lambda, \mu]}\) such that it is a Banach space and then we define and characterize those four-dimensional matrices which transform \(\mathcal{F}_{[\lambda, \mu]}\)-convergence of double sequences \(x = (x_{j k})\) into \(\mathcal{F}_{[\lambda, \mu]}\)-convergence. We also define a \(\mathcal{F}_{[\lambda, \mu]}\)-core of \(x = (x_{j k})\) and determine a Tauberian condition for core inclusions and core equivalence.

MSC:

40A05 Convergence and divergence of series and sequences

Citations:

Zbl 1469.40002
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References:

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