On the root-class residuality of certain HNN-extensions of groups

Let $\mathcal{K}$ be a root class of groups and $G$ be an HNN-extension of a group $B$ with subgroups $H$ and $K$ associated by an isomorphism $\varphi\colon H \to K$. We obtain certain sufficient conditions for $G$ to be residually a $\mathcal{K}$‑group provided the set $\{h^{-1}(h\varphi) \mid h \in H\}$ is a normal subgroup of $B$ or there exists an automorphism $\alpha$ of $B$ such that $H\alpha = K$. In particular, we find sufficient conditions for $G$ to be residually solvable, residually periodic solvable, or residually finite solvable in the case when $B$ is residually nilpotent while $H$ and $K$ are cyclic and map onto each other by an automorphism of $B$.