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.
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