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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 Δ 3 ,  B ( r, s, t ), Δ 2 ,  B ( r, s ) and Δ, where Δ 3 ,  B ( r, s, t ), Δ 2 ,  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.

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