Abstract
We develop new Banach sequence spaces e(0)(a,b) (p, q) and e(c)(a,b) (p, q) derived by the domain of generalized (p, q)-Euler matrix E-a,E-b (p, 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 alpha, beta, and gamma-duals of the spaces e(0)(a,b) (p, q) and e(c)(a,b) (p, q). Certain classes of matrix transformations are characterized from e(0)(a,b) (p, q) and e(c)(a,b) (p, q) to Z epsilon {l(infinity), (c), (c0), l(1), l(k)}. We obtain essential conditions of compactness of operators from e(0)(a,b) (p, q) and e(c)(a,b) (p, q) to Z epsilon {l(infinity), c, c(0), l(1), bs, cs, cs(0) }. Finally, under a definite functional rho and a weighted sequence of positive reals delta, we define a new sequence space (e(0)(a,b) (p, q, delta))(rho). 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.