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Some new sequence spaces defined by a modulus function. (English) Zbl 0946.46007
A function \(f\: [0,\infty)\to [0,\infty ]\) is called a modulus if (i) \(f(x)=0\) iff \(x=0\), (ii) \(f(x+y)\leq f(x)+f(y)\), (iii) \(f\) is increasing, (iv) \(f\) is continuous at \(0\). The author introduces three linear spaces \(w_0\subset w\subset w_{\infty }\) of sequences of complex numbers defined by conditions, where absolute value is replaced by a modulus function. He also shows that the spaces \(w_0\) and \(w\) are topological with a topology given by a paranorm.
It should be mentioned that there are two other papers by A. Esi (resp. A. ESi and M. Et) with the same title (neither of them contains references to the other two): [J. Inst. Math. Comput. Sci., Math. Ser. 8, No. 2, 81-86 (1995; Zbl 0843.46002), Pure Appl. Math. Sci. 43, No. 1-2, 95-99 (1996; Zbl 0892.46005)]. The results of the paper under review are more general.

46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
40C05 Matrix methods for summability
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