International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 11, Pages 741-752
doi:10.1155/S0161171200002088

Statistical limit point theorems

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 Ay 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.