Constraints on the Higgs boson self-coupling are set by combining the single Higgs boson analyses targeting the $\gamma \gamma$, $ZZ^*$, $WW^*$, $\tau^+ \tau^-$ and $b\bar{b}$ decay channels and the double Higgs boson analyses in the $b\bar{b}b\bar{b}$, $b\bar{b}\tau^+\tau^-$ and $b\bar{b} \gamma \gamma$ decay channels, using data collected at $\sqrt{s} = 13$ TeV with the ATLAS detector at the LHC. The data used in these analyses correspond to an integrated luminosity of up to 79.8 fb$^{-1}$ for single Higgs boson analyses and up to 36.1 fb$^{-1}$ for the double Higgs boson analyses. With the assumption that new physics affects only the Higgs boson self-coupling ($\lambda_{HHH}$), values outside the interval $-2.3<\lambda_{HHH}/\lambda_{HHH}^{\textrm{SM}}< 10.3$ are excluded at 95% confidence level. Results with less stringent assumptions are also provided, introducing additional coupling modifiers for the Higgs boson interactions with the other Standard Model particles.

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