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\(A\)-statistical core of a sequence. (English) Zbl 0959.40001

Author’s abstract: We extend the concepts of statistical limit superior and inferior (as introduced by Fridy and Orhan) to \(A\)-statistical limit superior and inferior and give some \(A\)-statistical analogue of properties of statistical limit superior and inferior for a sequence of real numbers. Also we extend the concept of statistical core to \(A\)-statistical core and get necessary and sufficient conditions on a matrix \(T\) so that the Knopp core of \(Tx\) is contained in the \(A\)-statistical core of a bounded complex number sequence \(x\).

MSC:

40A05 Convergence and divergence of series and sequences
26A03 Foundations: limits and generalizations, elementary topology of the line
11B05 Density, gaps, topology
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