  We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions,
defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This
deformation can be interpreted either as the introduction of a non-constant
curvature related to $\lambda$ on the underlying space or, equivalently, as a
Dunkl oscillator with a position-dependent mass function. This new quantum
model is shown to be exactly solvable in arbitrary dimension N, and its
eigenvalues and eigenfunctions are explicitly presented. Moreover, it is shown
that in the two-dimensional case both the Darboux III and the Dunkl oscillators
can be separately coupled with a constant magnetic field, thus giving rise to
two new exactly solvable quantum systems in which the effect of a
position-dependent mass and the Dunkl derivatives on the structure of the
Landau levels can be explicitly studied. Finally, the whole 2D Dunkl-Darboux
III oscillator is coupled with the magnetic field and shown to define an
exactly solvable Hamiltonian, where the interplay between the
$\lambda$-deformation and the magnetic field is explicitly illustrated.
