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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 $\alpha<\tau$, andoperators $\psi,\lambda:\ell^p\tau)\to\ell^p(\tau)$ we prove the generalizedshift$\mathop{\sigma_\varphi\restriction_{\ell^p(\tau)}:\ell^p(\tau)\to\ell^p(\tau)\:\:\:\:\:\:\:\:\:}\limits_{\:\:\:\:\:\:\:\:\:(x_\alpha)_{\alpha<\tau}\mapsto (x_{\varphi(\alpha)})_{\alpha<\tau}}$:  $\bullet$ is a $(\psi,\lambda)-$derivation if and only if there exists$\mathsf{r}\in{\mathbb C}^\tau$ with $\psi={\mathsfr}\sigma_\varphi\restriction_{\ell^p(\tau)}$ and$\lambda=((1)_{\alpha<\tau}-{\mathsfr})\sigma_\varphi\restriction_{\ell^p(\tau)}$,  $\bullet$ 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$\varphi=id_\tau$.

Generalized shifts through derivations' concept in $\ell^p(\tau)$ spaces