On Statistical Limit Points and the Consistency of Statistical Convergence

This article extends the concept of a statistical limit cluster.point of a sequence x as introduced by Fridy.to a T-statistical limit cluster. point, where T is a nonnegative regular matrix summability method. These definitions are reformulated in the setting of b N _ N. It is shown that for a bounded sequence x, the set of T-statistical cluster points of x forms a compact subset of R. It is also shown that, if T and R are two nonnegative regular summability matrices, then Tstatistical convergence and R-statistical convergence are consistent if and only if the support sets of T and R have nonempty intersection. Q 1996 Academic Press, Inc.