Four-dimensional generalized difference matrix and some double sequence spaces

Tuğ, Orhan (2017) Four-dimensional generalized difference matrix and some double sequence spaces. Journal of Inequalities and Applications, 149.

Text (Research Article) Tuǧ2017_Article_Four-dimensionalGeneralizedDif.pdf - Published Version Download (1MB)

Abstract

In this study, I introduce some new double sequence spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq) as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the spaces Mu, Cp, Cbp, Cr and Lq, respectively. I show that the double sequence spaces B(Mu), B(Cbp) and B(Cr) are the Banach spaces under some certain conditions. I give some inclusion relations with some topological properties. Moreover, I determine the α-dual of the spaces B(Mu) and B(Cbp), the β(ϑ)-duals of the spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq), where ϑ∈{p,bp,r}, and the γ-dual of the spaces B(Mu), B(Cbp) and B(Lq). Finally, I characterize the classes of four-dimensional matrix mappings defined on the spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq) of double sequences.

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