Patterson, Richard F.; Savas, Ekrem On double sequences of continuous functions having continuous P-limits. (English) Zbl 1289.40014 Publ. Math. Debr. 82, No. 1, 43-58 (2013). D. C. Gillespie and W. A. Hurwitz [Trans. Am. Math. Soc. 32, 527–543 (1930; JFM 56.0212.03)] proved the following result: If \(\left( s_{n}\right) \) is a sequence of functions continuous on a compact subset \(A\) of a metric space that converges pointwise to a continuous funtion \(s\) and is uniformly bounded on \(A,\) then there exists a regular nonnegative matrix \(T=\left( a_{nk}\right) \) (of a special type) such that \(\sum_{k}a_{nk}s_{k}\left( x\right) \rightarrow s\left(x\right) \) uniformly in \(x\in A\). The authors extend this result to double sequences of functions \(\left( s_{mn}\right) \) defined on \(A.\) Reviewer: Toivo Leiger (Tartu) Cited in 1 ReviewCited in 1 Document MSC: 40A30 Convergence and divergence of series and sequences of functions 40B05 Multiple sequences and series 40C05 Matrix methods for summability Keywords:\(RH\)-regular; double sequences; Pringsheim limit point; \(P\)-convergent; matrix methods of summability Citations:JFM 56.0212.03 PDFBibTeX XMLCite \textit{R. F. Patterson} and \textit{E. Savas}, Publ. Math. Debr. 82, No. 1, 43--58 (2013; Zbl 1289.40014) Full Text: DOI