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Some Difference Paranormed Sequence Spaces over n-normed Spaces Defined by a Musielak-Orlicz Function

  • Raj, Kuldip ;
  • Sharma, Sunil K. ;
  • Gupta, Amit
  • Received : 2011.08.18
  • Accepted : 2012.08.22
  • Published : 2014.03.23

Abstract

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

Keywords

Paranorm space;difference sequence spaces;Orlicz function;Musielak-Orlicz function;solid;monotone etc

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