Hokkaido Mathematical Journal

ALTIN Yavuz, I\C{S}IK Mahmut,

On some new seminormed sequence spaces defined by modulus functions.

Hokkaido Mathematical Journal, 35 (2006) pp.565-572

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Abstract

In this paper we introduce the sequence spaces $\ell _{\infty }(f,p,\sigma ,q,s),c_{0}(f,p,\sigma ,q,s)$ and $c(f,p,\sigma ,q,s)$ using a modulus function $f$ and defined over a seminormed space$(X,q)$, seminormed by $q$. We study some properties of these sequence spaces and obtain some inclusion relations.

MSC(Primary)40C05
MSC(Secondary)40D05, 40A05
Uncontrolled Keywordsmodulus function, invariant mean, seminorm