On the Statistical Convergence of Order α in Paranormed Space

The aim of the present work is to introduce notions of statistical convergence, strongly p-Cesàro summability and the statistically Cauchy sequence of order α in paranormed spaces. Some certain topological properties of these new concepts are examined. Furthermore, we introduce the some inclusion relations among them.

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 Product Normed Space Valued Paranormed Space of Summable Sequences

The aim of this paper is to introduce and study a new vector valued sequence space S( ( Z, || ( . , . ) ||Z ), ?, u ) with terms from a product normed space as a generalization of sequence space studied by Srivastava and Pahari (2011) which is itself the generalization of the familiar absolutely summable sequence space l. We investigate its linear structure with respect to the co-ordinate wise vector operation and explore the conditions in terms of different u and ? so that a class is contained in another class of same kind and thereby derive the conditions of their equality. Finally we investigate the paranormed structure of S ( ( Z, || (. , . ) ||Z ), ?, u ) by endowing it with a suitable natural paranorm.Journal of Institute of Science and Technology, 2014, 19(1): 25-29

λ-Statistical Convergence in Paranormed Space

The concept ofλ-statistical convergence for sequences of real numbers was introduced in Mursaleen (2000). In this paper, we prove decomposition theorem forλ-statistical convergence. We also define and studyλ-statistical convergence,λ-statistically Cauchy, and stronglyλp-summability in Paranormed Space.