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

In this work, we construct the sequence spaces ${\displaystyle f\left(Q(r,s,t,u)\right)}$, ${\displaystyle f_0\left(Q(r,s,t,u)\right)}$ and ${\displaystyle f_s\left(Q(r,s,t,u)\right)}$, where ${\displaystyle Q(r,s,t,u)}$ is quadruple band matrix which generalizes the matrices ${\displaystyle {\Delta }^3}$, ${\displaystyle B(r,s,t)}$, ${\displaystyle {\Delta }^2}$, ${\displaystyle B(r,s)}$ and ${\displaystyle \Delta }$, where ${\displaystyle {\Delta }^3}$, ${\displaystyle B(r,s,t)}$, ${\displaystyle {\Delta }^2}$, ${\displaystyle B(r,s)}$ and ${\displaystyle \Delta }$ 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 ${\displaystyle f}$, ${\displaystyle f_0}$ and ${\displaystyle f_s}$, respectively. Moreover, we give the Schauder basis and ${\displaystyle \beta }$-, ${\displaystyle \gamma }$-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.