  We study the effects of strong magnetic fields on antikaon condensation in
neutron star matter using the quark-meson coupling (QMC) model. The QMC model
describes a nuclear many-body system as nonoverlapping MIT bags in which quarks
interact through the self-consistent exchange of scalar and vector mesons in
the mean-field approximation. It is found that the presence of strong magnetic
fields alters the threshold density of antikaon condensation significantly. The
onset of $K^-$ condensation stronger depends on the magnetic field strength,
and it even shifts beyond the threshold of $\bar K^0$ condensation for
sufficiently strong magnetic fields. In the presence of strong magnetic fields,
the equation of state (EOS) becomes stiffer in comparison with the field-free
case. The softening of the EOS by antikaon condensation also depends on the
magnetic field strength, and it becomes less pronounced with increasing
magnetic field strength. The results of the QMC model are compared with those
obtained in a relativistic mean-field (RMF) model, and we find there are
quantitative differences between the results of the QMC and RMF models.
