Original scientific paper

An interesting example concerning convergence of double sequences

H. I. Miller
Wieren L. Miller-Van

Abstract

In a paper recently submitted for publication, it was shown in Theorem 5,that if $s= ( s_{ij})$ is a divergent double sequence and $A= (A^{pq})$is a double sequence of matrix summability methods \footnote{satisfying certain specified conditions}, then the set of "subsequences'' of $s$ that are statistically $A$ convergent is of the first Baire category in the set of all "subsequences'' of $s$.
The main result in this paper shows that the above mentioned result is no longer true if $A$ does not satisfy the last of the four conditions on $A$ in Theorem $5$ of \cite{7}. Other related matters are considered.

Keywords

statistical convergence; double sequences

Hrčak ID:

640

URI

https://hrcak.srce.hr/640

Publication date:

27.12.2005.

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