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Zbl 0631.46010
Maddox, Ivor J.
Sequence spaces defined by a modulus. (English)
[J] Math. Proc. Camb. Philos. Soc. 100, 161-166 (1986). ISSN 0305-0041; ISSN 1469-8064/e

f: [0,$\infty)\to [0,\infty)$ is called a modulus if (i) $f(x)=0$ iff $x=0$, (ii) $f(x+y)\le f(x)+f(y)$ for x,y$\ge 0$, (iii) f is increasing, (iv) f is continuous. \par Using the modulus f, the author introduces and studies three sequence spaces $w\sb 0(f)$, w(f), $w\sb{\infty}(f)$ which generalizes the spaces $w\sb 0$, w, $w\sb{\infty}$ of strongly summable sequences. Besides other results, it is shown that $w\sb 0(f)$ and w(f) are paranormed FK spaces.
[C.Zălinescu]

MSC 2000:: *46A45 Sequence spaces

Keywords: modulus; sequence spaces; paranormed FK spaces

Cited in: Zbl 1163.47048 Zbl 1099.46004 Zbl 1030.40003 Zbl 1021.46020 Zbl 0937.46004 Zbl 0914.46005 Zbl 0808.40007 Zbl 0674.40008

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