  Let $T\in B(H)$ be a bounded linear operator on a Hilbert space $H$, let $T =
V|T|$ be its polar decomposition of $T$ and let $\lambda\in [0,1]$. The
$\lambda$-Aluthge transform $\Delta_{\lambda}(T)$ and the mean transforms
$M(T)$ are defined respectively by:
\[\Delta_{\lambda}(T):=|T|^{\lambda}V|T|^{1-\lambda} \;\; \text{and} \;\;
M(T):=\frac12(|T|V+V|T|).\] In this paper, we use several examples of weighted
shift operators to prove that the Aluthge and mean transforms do not preserve
the class of $m-$isometries in any directions.
