Mappings Ideal of Type the Domain of Generalized p,q-Euler Matrix in c0 and c

Abstract

We develop new Banach sequence spaces e0a,bp,q and eca,bp,q derived by the domain of generalized p,q-Euler matrix Ea,bp,q in the spaces of null and convergent sequences, respectively. We investigate some topological properties and inclusion natures related to these spaces. We construct bases and obtain α, β, and γ-duals of the spaces e0a,bp,q and eca,bp,q. Certain classes of matrix transformations are characterized from e0a,bp,q and eca,bp,q to Z∈ℓ∞,c,c0,ℓ1,ℓk. We obtain essential conditions of compactness of operators from e0a,bp,q and eca,bp,q to Z∈ℓ∞,c,c0,ℓ1,bs,cs,cs0. Finally, under a definite functional ϱ and a weighted sequence of positive reals δ, we define a new sequence space e0a,bp,q,δϱ. Certain geometric and topological properties of this space along with the eigenvalue distribution of mapping ideals due to this space and s-numbers are investigated.