  We have investigated properties of $\alpha$-decay chains of recently produced
superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with
inclusion of the vector self-coupling of $\omega$ meson in the framework of the
relativistic mean-field theory. It is shown that the experimentally observed
alpha-decay energies and half-lives are reproduced well by this Lagrangian
model. Further calculations for the heavier elements with Z=117-125 show that
these nuclei are superdeformed with a prolate shape in the ground state. A
superdeformed shell-closure at Z=118 lends an additional binding and an extra
stability to nuclei in this region. Consequently, it is predicted that the
corresponding $Q_\alpha$ values provide $\alpha$-decay half-lives for heavier
superheavy nuclei within the experimentally feasible conditions. The results
are compared with those of macroscopic-microscopic approaches. A perspective of
the difference in shell effects amongst various approaches is presented and its
consequences on superheavy nuclei are discussed.
