Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness (Q1021643)

Recently \textit{C. Adydin} and \textit{F. Başar} [Appl. Math. Comput. 157, No.~3, 677--693 (2004; Zbl 1072.46007)] studied the matrix domain of a triangular matrix in the sets of sequences that are (i) summable to zero, (ii) summable and (iii) bounded by the Cesàro method of order one. \textit{I. J. Maddox} [J. Lond. Math. Soc. 43, 285-290 (1968; Zbl 0155.38802)] introduced and studied the above-mentioned class of sequences by the strong Cesàro method of order 1 with index \(p\), \(p\geq 1\). Here the authors discuss the class of sequences studied by C. Adydin and F. Basar for the strong Cesàro method of order 1 with index \(p\), \(p\geq 1\). They also determine the \(\beta\)-duals of the spaces studied and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.