  Exact solution of Dirac equation for a particle whose potential energy and
mass are inversely proportional to the distance from the force centre has been
found. The bound states exist provided the length scale $a$ which appears in
the expression for the mass is smaller than the classical electron radius
$e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$
even in the absence of the Coulomb interaction. Quasirelativistic expansion of
the energy has been carried out, and a modified expression for the fine
structure of energy levels has been obtained. The problem of kinetic energy
operator in the Schr\"odinger equation is discussed for the case of
position-dependent mass. In particular, we have found that for highly excited
states the mutual ordering of the inverse mass and momentum operator in the
non-relativistic theory is not important.
