Statistical limit point theorems

Jeff Zeager

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-12

Abstract:

It is known that given a regular matrix A and a bounded sequence x there is a subsequence (respectively, rearrangement, stretching) y of x such that the set of limit points of A y includes the set of limit points of x . Using the notion of a statistical limit point, we establish statistical convergence analogues to these results by proving that every complex number sequence x has a subsequence (respectively, rearrangement, stretching) y such that every limit point of x is a statistical limit point of y . We then extend our results to the more general A -statistical convergence, in which A is an arbitrary nonnegative matrix.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:654014

DOI: 10.1155/S0161171200002088

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