In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz -difference sequence space , . For this purpose, we apply the Hausdorff measure of noncompactness and use some results.

In this article we introduce some new difference sequence spaces with a real 2-normed linear space as base space and which are defined using a sequence of Orlicz functions, a bounded sequence of positive real numbers and a sequence of non-zero reals as multiplier sequence. We show that these spaces are complete paranormed spaces when the base space is a 2-Banach space and investigate these spac...

in this paper we introduce entire sequence spaces defined by a sequence of modulus functions . we study some topological properties of these spaces and prove some inclusion relations.

and Applied Analysis 3 2. The Sequence Space λ, p In this section, we define the sequence space λ, p and prove that this sequence space according to its paranorm is complete paranormed linear space. In 1 , Mursaleen and Noman defined the matrix Λ λnk ∞ n,k 0 by λnk ⎧ ⎨ ⎩ λk − λk−1 λn 0 ≤ k ≤ n 0 k > n , 2.1 where λ λk ∞ k 0 is a strictly increasing sequence of positive reals tending to ∞, that ...

The paper investigates some classes of real number sequences over 2-normed spaces defined by means of Orlicz functions, a bounded sequence of strictly positive real numbers, a multiplier and a normal paranormed sequence space. Relevant properties of such classes have been investigated. Moreover, relationships among different such classes of sequences have also been studied under various paramet...