A study of $CP$ violation in $B^mp rightarrow Dh^mp$ ($h=K,pi$) with the modes $D rightarrow K^mp pi^pm pi^0$, $D rightarrow pi^+pi^-pi^0$ and $D rightarrow K^+K^-pi^0$

An analysis of the decays of $B^mp rightarrow D K^mp$ and $B^mp rightarrow D pi^mp $ is presented in which the $D$ meson is reconstructed in the three-body final states $K^mp pi^pm pi^0$, $pi^+ pi^- pi^0$ and $K^+ K^- pi^0$. Using data from LHCb corresponding to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collisions, measurements of several $CP$ observables are performed. First observations are obtained of the suppressed ADS decay $B^mp rightarrow [pi^mp K^pm pi^0]_D pi^mp$ and the quasi-GLW decay $B^mp rightarrow [K^+ K^- pi^0]_D pi^mp$. The results are interpreted in the context of the unitarity triangle angle $gamma$ and related parameters.