Constraints on the Higgs boson self-coupling are set by combining 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 with the single-Higgs boson analyses targeting the $\gamma \gamma$, $ZZ^*$, $WW^*$, $\tau^+ \tau^-$ and $b\bar{b}$ final states. The data used by these analyses were recorded by the ATLAS detector at the LHC in proton-proton collisions at $\sqrt{s}=13$ TeV and correspond to an integrated luminosity of 126-139 fb$^{-1}$. The combination of the double-Higgs analyses sets an upper limit at 95\% confidence level on the production cross section of this process normalised to its Standard Model prediction $\mu_{HH} < 2.4$. Combining the single-Higgs and double-Higgs analyses, with the assumption that new physics affects only the Higgs boson self-coupling ($\lambda_{HHH}$), values outside the interval $-0.4< \kappa_{\lambda} =(\lambda_{HHH}/\lambda_{HHH}^{\textrm{SM}})< 6.3$ are excluded at 95\% confidence level. The combined single-Higgs and double-Higgs analyses also allow the provision of results with fewer model-dependent assumptions, where additional coupling modifiers for the Higgs boson interactions with the other Standard Model particles are also introduced.

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