  An algebraic analysis framework for quantum calculus is proposed. The quantum
derivative operator $D_{\tau ,\sigma}$ is based on two commuting bijections
$\tau$ and $\sigma$ defined on an arbitrary set $M$ equipped with a tension
structure determined by a single tension function $\theta$, i.e. a
1-dimensional case is analyzed here. The well known cases, i.e. $h$- and
$q$-calculi together with their symmetric versions, can be obtained owing to
special choice of mappings $\tau$ and $\sigma$.
