Arithmetic summable sequence space over non-Newtonian field

Abstract

Recently Ruckle \cite{RuckleArithmeticalSummability} introduced the theory of arithmetical summability suggested by the sum ${\sum }_{k|m}f(k)$ as $k$ ranges over the divisors of $m$ including $1$ and $m.$ 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.

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