  We examine the bound state solutions of the Dirac equation under the spin and
pseudospin symmetries for a new suggested combined potential, Hulten plus a
class of Yukawa potential including a Coulomb-like tensor interaction. An
improved scheme is employed to deal with the centrifugal (pseudo-centrifugal)
term. Using the Nikiforov-Uvarov and SUSYQM methods, we analytically develop
the relativistic energy eigenvalues and associated Dirac spinor components of
wave functions. We find that both methods give entirely the same results.
Modifiable of our results into some particular potential cases, useful for
other physical systems, are also discussed. We obtain complete agreement with
the findings of previous works. The spin and pseudospin bound state energy
spectra for various levels are presented in the absence as well as the presence
of tensor coupling. Both energy spectrums are sensitive with regards to the
quantum numbers $\kappa$ and $n$, as well as the parameter $\delta$. We also
notice that the degeneracies between Dirac spin and pseudospin doublet
eigenstate partners are completely removed by the tensor interaction. Finally,
we present the parameter space of allowable bound state regions of potential
strength $V_0$ with constants for both considered symmetry limits $C_S$ and
$C_{PS}$.
