  The recent discovery of a Higgs boson at LHC, while establishing the Higgs
mechanism as the way of electroweak symmetry breaking, started an era of
precision measurements involving the Higgs boson. In an effective Lagrangian
framework, we consider the e+e- --> ZHH process, at an ILC running at a centre
of mass energy of 800 GeV to investigate the effect of the ZZH and ZZHH
couplings on the sensitivity of HHH coupling on this process. Our results show
that the sensitivity of the trilinear Higgs self couplings on this process has
somewhat strong dependence on the Higgs-gauge boson couplings. Single and two
parameter reach of ILC with integrated luminosity of 1000 /fb are obtained on
the effective couplings, c6 and cH, which are related to the HHH couplings,
indicating how these limits are affected by the presence of anomalous ZZH and
ZZHH couplings. The kinematic distributions studied to understand the effect of
the anomalous couplings, again, show strong influence of Z-H couplings on the
dependence of these distributions on HHH coupling. Similar results are
indicated in the case of the process, e+e- --> nu nu HH, considered at a centre
of mass energy of 2 TeV, where the cross section is large enough. The effect of
WWH and WWHH couplings on the sensitivity of HHH coupling is clearely
established through our analyses of this process.
