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Sequence spaces defined by a modulus. (English) Zbl 0631.46010
f: [0,$$\infty)\to [0,\infty)$$ is called a modulus if (i) $$f(x)=0$$ iff $$x=0$$, (ii) $$f(x+y)\leq f(x)+f(y)$$ for x,y$$\geq 0$$, (iii) f is increasing, (iv) f is continuous.
Using the modulus f, the author introduces and studies three sequence spaces $$w_ 0(f)$$, w(f), $$w_{\infty}(f)$$ which generalizes the spaces $$w_ 0$$, w, $$w_{\infty}$$ of strongly summable sequences. Besides other results, it is shown that $$w_ 0(f)$$ and w(f) are paranormed FK spaces.
Reviewer: C.Zălinescu

##### MSC:
 46A45 Sequence spaces (including Köthe sequence spaces)
##### Keywords:
modulus; sequence spaces; paranormed FK spaces
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##### References:
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