  We investigate the approximate solutions of the Dirac equation with the
position-dependent mass particle in the Eckart potential field including the
Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method.
Taking an appropriate approximation to deal with the centrifugal term, the
Dirac energy states and the corresponding normalized two-spinor components of
the wave function are obtained in closed form. Some special cases of our
solution are investigated. Furthermore, we present the correct solutions
obtained via the asymptotic iteration method which are in agreement with the
parametric Nikiforov-Uvarov method results.
