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On some new sequence spaces and related matrix transformations. (English) Zbl 0855.40005

Author’s abstract: The sequence spaces \(l(p)\), \(l_\infty (p)\), \(c_0 (p)\) and \(c(p)\) were defined by Maddox, Simons and Nakano. Recently Bulut and Çakar defined the sequence space \(l(p, s)\). In this paper, our main purpose is to define and investigate the sequence spaces \(l_\infty (p, s)\), \(c_0 (p, s)\) and \(c(p, s)\) and to determine the necessary and sufficient conditions to characterize \((l_\infty (p, s), l_\infty)\), \((l_\infty (p, s), c)\), \((c(p, s), c)\), \((c_0 (p, s), c)\), \((c_0 (p, s), l_\infty (p, s))\) and \((c_0 (p, s), c_0 (q, s))\) matrices.
Reviewer: J.Boos (Hagen)

MSC:

40C05 Matrix methods for summability
46A45 Sequence spaces (including Köthe sequence spaces)
40D25 Inclusion and equivalence theorems in summability theory
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