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