Serkan Demiriz

Some Topological and Geometrical Properties of a New Difference Sequence Space

We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and l𝑝 are linearly isomorphic for 1≤𝑝l∞. Furthermore, the basis and the 𝛼-, 𝛽- and 𝛾-duals of the space 𝑎𝑟𝑝(Δ) are determined. We devote the final section of the paper to examine some geometric properties of the space 𝑎𝑟𝑝(Δ).

Some topological and geometrical properties of the sequence space er (u,p)

Abstract In this paper, we introduce the sequence space e r ( u,p ) and investigate its some topological and geometrical properties such as basis, α-, β-, γ- duals and the uniform Opial property.

Domain of the Generalized Double Cesàro Matrix in Some Paranormed Spaces of Double Sequences

Abstract In this paper, we investigate some double paranormed sequence spaces which are domain of the double generalized Cesàro matrix Rq in some double sequence spaces. We also determined of α-dual of Ru(t) which is the space of double sequences whose Rq-transforms are bounded and examined some linear and topological properties of these sequence spaces.

On Some New Generalized Difference Sequence Spaces of Nonabsolute Type

We define a new triangle matrix by the composition of the matrices and . Also, we introduce the sequence spaces , and by using matrix domain of the matrix on the classical sequence spaces , and , respectively, where . Moreover, we show that the space is norm isomorphic to for . Furthermore, we establish some inclusion relations concerning those spaces and determine -, -, and -duals of those spaces and construct the Schauder bases , and . Finally, we characterize the classes of infinite matrices where and .