Mozyraska-Torres logarithm is negative on (0,1)

Theorem

Let $\mathbb{T}$ be a time scale. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$, where $L_{\mathbb{T}}$ denotes the Mozyrska-Torres logarithm.

References

Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)