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Zbl 1171.40002
Altay, Bilâl; Başar, Feyzi; Malkowsky, Eberhard
Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness.
(English)
[J] Appl. Math. Comput. 211, No. 2, 255-264 (2009). ISSN 0096-3003

Recently {\it C. Adydin} and {\it 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. {\it 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.
[Ganesh Datta Dikshit (Auckland)]
MSC 2000:
*40C05 Matrix methods in summability
40H05 Functional analytic methods in summability

Keywords: matrix domain in a sequence space; $\beta$-duals; triangular matrix transformations; strong Cesàro summability with index

Citations: Zbl 1072.46007; Zbl 0155.38802

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