Pre-differentiable

Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mathbb{T}^{\kappa}$ if $f$ is delta differentiable at all $t \in D$ and $\mathbb{T}^{\kappa} \setminus D$ is countable and contains no right-scattered points in $\mathbb{T}$.

References

• Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Definition $1.62$
• Dorota Mozyrska and Ewa Pawluszewicz: Functional series on time scales (2008)... (previous)... (next)