  We study an special law for the deceleration parameter, recently proposed by
Akarsu and Dereli, in the context of $f(R)$, $f(T)$ and $f(\mathcal{G})$
theories of modified gravity. This law covers the law of Berman for obtaining
exact cosmological models to account for the current acceleration of the
universe, and also gives the opportunity to generalize many of the dark energy
models having better consistency with the cosmological observations. Our aim is
to reconstruct the $f(R)$, $f(T)$ and $f(\mathcal{G})$ models inspired by this
law of variable deceleration parameter. Such models may then exhibit better
consistency with the cosmological observations.
