Some Topological and Geometrical Properties of a New Difference Sequence Space

Abstract

We introduce the new difference sequence space . Further, it is proved that the space is the BK-space including the space , which is the space of sequences of pbounded variation. We also show that the spaces , and are linearly isomorphic for . Furthermore, the basis and the , and duals of the space are determined. We devote the final section of the paper to examine some geometric properties of the space .

Certain Geometric Properties and Matrix Transformations on a Newly Introduced Banach Space

“…For instance, Mursaleen et al [7] examined the geometric properties of Euler sequence space. More information about the relevant literature can be found in [8]- [14].…”

Some B-difference sequence spaces derived by generalized means and compact operators

“…V. if r n = n + 1, t n = 1 + α n , where 0 < α < 1, s n = 1 ∀n, u = 1, v = −1, then the sequence space l p (r, s, t; B) reduces to the sequence space a α p (∆) studied by Demiriz and Ç akan [7].…”

Fark Seri Uzayları ve Matris Dönüşümleri

“…Recently, there has been a lot of intrest in studies on the sequence spaces. In the literature, the basic concept is to generate new sequence spaces by means of the matrix domain of triangles (see, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Besides this, several authors have studied difference sequence spaces using some newly defined infinite matrices.…”