On the Domain of Four-Dimensional Forward Difference Matrix in Some Double Sequence Spaces

2021/12/18 by Tug, Orhan, Malkowsky, Eberhard, Rakocevic, Vladimir +1
#40C05 #46A45 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2112.09909

Abstract

In this paper, we introduce some new double sequence spaces M_u(Δ) and C_ϑ(Δ), where ϑ∈\bp,bp0,r,r0\ as the domains of the four-dimensional forward difference matrix in the double sequence spaces M_u and C_ϑ, respectively. Then we investigate some topological and algebraic properties. Moreover, we determine the α-, β(ϑ)-, and γ-duals of the new spaces M_u(Δ) and C_ϑ(Δ). Finally, we characterize four-dimensional matrix classes (λ(Δ),μ) and (μ,λ(Δ)), where λ=\M_u,C_ϑ\ and μ=\M_u,C_ϑ\.

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