  In the following text for $p\in[1,\infty]$, nonzero cardinal number $\tau$,
self--map $\varphi:\tau\to\tau$ if there exists $N\in\mathbb{N}$ such that
$\varphi^{-1}(\alpha)$ has at most $N$ elements for each $\alpha<\tau$, and
operators $\psi,\lambda:\ell^p\tau)\to\ell^p(\tau)$ we prove the generalized
shift
$\mathop{\sigma_\varphi\restriction_{\ell^p(\tau)}:\ell^p(\tau)\to\ell^p(\tau)\:\:\:\:\:\:\:\:\:}\limits_{\:\:\:\:\:\:\:\:\:
(x_\alpha)_{\alpha<\tau}\mapsto (x_{\varphi(\alpha)})_{\alpha<\tau}}$:
  $\bullet$ is a $(\psi,\lambda)-$derivation if and only if there exists
$\mathsf{r}\in{\mathbb C}^\tau$ with $\psi={\mathsf
r}\sigma_\varphi\restriction_{\ell^p(\tau)}$ and
$\lambda=((1)_{\alpha<\tau}-{\mathsf
r})\sigma_\varphi\restriction_{\ell^p(\tau)}$,
  $\bullet$ is a $\psi-$derivation if and only if
$\psi=\frac12\sigma_\varphi\restriction_{\ell^p(\tau)}$,
  $\bullet$ is not a (Jordan, Jordan triple) derivation,
  $\bullet$ is a generalized (Jordan, Jordan triple) derivation if and only if
$\varphi=id_\tau$.
