On a result of Flett for Cesàro matrices (Q847271)

The results in the paper extend the related results of \textit{T. M. Flett} [Proc. Lond. Math. Soc., III. Ser. 7, 113--141 (1957; Zbl 0109.04402)] and \textit{E. Savas} and \textit{H. Sevli} [Appl. Math. Lett. 20, No. 4, 476--478 (2007; Zbl 1166.40005)]. The author mainly finds sufficient conditions for a lower triangular matrix \(T=(t_{nj})\) to ensure that the condition \(\sum^{\infty}_{n=1} \alpha_{n}|s_{n}-s_{n-1}|^{k} < \infty\) implies that \(\sum^{\infty}_{n=1} \beta_{n}|t_{n}-t_{n-1}|^{s} < \infty\) where \(t_{n}=\sum^{n}_{j=0} t_{nj}s_{j}\), and \((\alpha_n)\) and \((\beta_n)\) are positive sequences and \(k>0\), \(s\geq{1}\).