  We have discussed the correspondence of the well-accepted $f(G)$ gravity
theory with two dark energy models : $(m,n)$-type holographic dark energy
[$(m,n)$-type HDE] and entropy-corrected $(m,n)$-type holographic dark energy.
For this purpose, we have considered the power law form of the scale factor
$a(t)=a_{0}t^{p}, p>1$. The reconstructed $f(G)$ in these models have been
found and the models in both cases are found to be realistic. We have also
discussed the classical stability issues in both models. The $(m,n)$-type HDE
and its entropy-corrected versions are more stable than the ordinary HDE model.
