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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)

40C05Matrix methods in summability
46A45Sequence spaces
40D25Inclusion theorems; equivalence theorems