On some new paranormed difference sequence spaces defined by Orlicz functions. (English) Zbl 1208.46005

Summary: The main aim of this article is to introduce a new class of sequence spaces using the concept of \(n\)-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to the derived \((n-1)\)-norm. We use an Orlicz function, a bounded sequence of positive real numbers and some difference operators to construct these spaces so that they become more generalized and some other spaces can be derived under special cases. These investigations will enhance the acceptability of the notion of \(n\)-norm by giving a way to construct different sequence spaces with elements in \(n\)-normed spaces.


46A45 Sequence spaces (including Köthe sequence spaces)
46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
40A05 Convergence and divergence of series and sequences
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