Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, vol.0, no.0, 2020 (ESCI)
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 Delta(3), B(r, s, t), Delta(2), B(r, s) and Delta, where Delta(3), B(r, s, t), Delta(2), B(r, s) and Delta 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 f(s), respectively. Moreover, we give the Schauder basis and beta, gamma-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.