  Let $(M,\omega)$ be an aspherical symplectic manifold, which is closed or
convex. Let $U$ be an open set in $M$, which admits a circle action generated
by an autonomous Hamiltonian $H \in C^\infty(U)$, such that each orbit of the
circle action is not contractible in $M$. Under these assumptions, we prove
that the Hofer-Zehnder capacity of $U$ is bounded by the Hofer norm of $H$. The
proof uses a variant of the energy-capacity inequality, which is proved by the
theory of action selectors.
