The root class residuality of the tree product of groups with amalgamated retracts

Given a root class $\mathscr{K}$ of groups, we prove that the tree product of residually $\mathscr{K}$-groups with amalgamated retracts is a residually $\mathscr{K}$-group. This yields a criterion for the $\mathscr{K}$-residuality of Artin and Coxeter groups with tree structure. We also prove that the HNN-extension $X$ of a residually $\mathscr{K}$-group $B$ is a residually $\mathscr{K}$-group provided that the associated subgroups of $X$ are retracts in $B$ and $\mathscr{K}$ contains at least one nonperiodic group.