  Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{P}_{n}$ be the
semigroup of partial transformations on $[n]$. Let
$\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: (for ~all~x,y\in
Dom~\alpha)~|x\alpha-y\alpha|\leq|x-y|\}$ be the subsemigroup of partial
contraction mappings on $[n]$. We have shown that the semigroup
$\mathcal{CP}_{n}$ and some of its subsemigroups are nonregular left abundant
semigroups for all $n$ but not right abundant for $n\geq 4$.
