Almost convergent sequence spaces derived by the domain of quadruple band matrix

In this work, we construct the sequence spaces f(Q(r, s, t, u)), f₀(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ³, B(r, s, t), Δ², B(r, s) and Δ, where Δ³, B(r, s, t), Δ², B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f₀ and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.