Arithmetic summable sequence space over non-Newtonian field

Recently Ruckle \cite{RuckleArithmeticalSummability} introduced the theory of arithmetical summability suggested by the sum ${\sum }_{k\mathrm{\mid }m}f(k)$ as $k$ ranges over the divisors of $m$ including $1$ and $m\mathrm{.}$ Following Ruckle \cite{RuckleArithmeticalSummability} we construct the sequence space $AS(G)$ and $AC(G)$ of arithmetic summable and arithmetic convergent sequences in the sense of geometric calculus and derive interesting results in the geometric field.