Abstract
Abstract In this work, we construct the sequence spaces f(Q(r, s, t, u)), f 0(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, f 0 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.
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