We introduce new Banach spaces eα,β0 (q) and e α,β c (q) defined as the domain of generalized q-Euler matrix Eα,β(q) in the spaces c0 and c, respectively. Some topological properties and inclusion relations related to the newly defined spaces are exhibited. We determine the bases and obtain Köthe duals of the spaces eα,β0 (q) and e α,β c (q). We characterize certain matrix mappings from the spaces e α,β 0 (q) and e α,β c (q) to the space S ∈ {ℓ∞, c, c0, ℓ1, bs, cs, cs0}. We compute necessary and sufficient conditions for a matrix operator to be compact from the space eα,β0 (q) to the space S ∈ {ℓ∞, c, c0, ℓ1, bs, cs, cs0} using Hausdorff measure of non-compactness. Finally, we give point spectrum of the matrix Eα,β(q) in the space c.