On the paranormed space L(t) of double sequences

In this paper, we introduce the paranormed sequence space L(t) which is the generalization of the space Lq of all absolutely q-summable double sequences. We examine some topological properties of the space L(t) and determine its alpha-, beta- and gamma-duals. Finally, we characterize some classes of four-dimensional matrix transformations from the space L(t) into some spaces of double sequences.

On the paranormed space $\mathcal{M}_{u}(t)$ of double sequences

In this paper, we introduce the paranormed sequence space $\mathcal{M}_{u}(t)$ corresponding to the normed space $\mathcal{M}_{u}$ of bounded double sequences. We examine general topological properties of this space and determine its alpha-, beta- and gamma-duals. Furthermore, we characterize some classes of four-dimensional matrix transformations concerning this space and its dual spaces.

On Certain Topological Structures of Summable Paranormed Sequence Space Defined in Two - Normed Space

on PDFJournal of Institute of Science and Technology, 2014, 19(2): 135-140

On Some Geometric Properties of a New Paranormed Sequence Space

We introduce a new sequence space which is defined by the operatorW=(wnk)on the sequence spaceℓ(p). We define a modular functional on this space and investigate structure of this space equipped with Luxemburg norm. Also we study some geometric properties which are called Kadec-Klee, k-NUC, and uniform Opial properties and prove that this new space possesses these properties.

On Vector Valued Paranormed Sequence Space l (X,M, ?, p,L) Defined by Orlicz Function

DOI: http://dx.doi.org/10.3126/njst.v12i0.6510 Nepal Journal of Science and Technology 12 (2011) 252-259