International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 11, Pages 741-752

Statistical limit point theorems

Jeff Zeager

Division of Science and Mathematics, Lorain County Community College, Elyria 44035, Ohio, USA

Received 4 August 1998

Copyright © 2000 Jeff Zeager. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.