  We investigate the implication of the recent discovery of a Higgs-like
particle in the first phase of the LHC Run 1 on the Inert Higgs Doublet Model
(IHDM). The determination of the Higgs couplings to SM particles and its
intrinsic properties will get improved during the new LHC Run 2 starting this
year. The new LHC Run 2 would also shade some light on the triple Higgs
coupling. Such measurement is very important in order to establish the details
of the electroweak symmetry breaking mechanism. Given the importance of the
Higgs couplings both at the LHC and $e^+e^-$
  Linear Collider machines, accurate theoretical predictions are required. We
study the radiative corrections to the triple Higgs coupling $hhh$ and to
$hZZ$, $hWW$ couplings in the context of the IHDM. By combining several
theoretical and experimental constraints on parameter space, we show that extra
particles might modify the triple Higgs coupling near threshold regions.
Finally, we discuss the effect of these corrections on the double Higgs
production signal at the $e^+e^-$ LC and show that they can be rather
important.
