On the Riesz difference sequence space

Abstract

In the present paper, we define the difference sequence space r q (p, Δ ), which is defined as follows:where r q (p) is the Riesz sequence space given by Altay and Başar. We give some topological properties and compute the α−, β − duals of this space.

Compact Operators for Almost Conservative and Strongly Conservative Matrices

“…This technique has recently been used by several authors in many research papers (cf. [8][9][10][11][12][13][14]). Further the technique of measures of noncompactness has also been used in solving the infinite system of differential equations in some sequence spaces (see [15][16][17]).…”

A different approach for almost sequence spaces defined by a generalized weighted means

“…[21] xi) = ( ) ∈ ( : ) necessary and sufficient condition (27) and (28) yield. [22] xii) = ( ) ∈ ( : ) necessary and sufficient condition (30) and (33) yield. [23] Corollary 2: The following statements hold: i) = ( ) ∈ ( ( , ): ) necessary and sufficient condition { } ∈ℕ ∈ ( , ) for all ∈ ℕ and (15) yields with lieu of .…”

“…iii) = ( ) ∈ ( ( , ): ) necessary and sufficient condition { } ∈ℕ ∈ ( , ) for all ∈ ℕ and (30) yields. iv) = ( ) ∈ ( ( , ): ) necessary and sufficient condition { } ∈ℕ ∈ ( , ) for all ∈ ℕ and (30), (33) yield with lieu of .…”

“…[32] [33] [34][35],[36]. Recently, A. Karaisa and F. Özger[12] the spaces ( , , ∆), ( , , ∆) and ( , , ∆) defined and studied.…”

A new perspective on paranormed Riesz sequence space of non-absolute type

“…Moreover, the ones who are more interested in the subject are advised to read [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. We should note here, there are many different ways to construct new sequence spaces from old ones.…”