  We consider the eigenvalue problem associated with the Dunkl-type
differential operator (in which the reflection operator R is involved) L = dx R
+ v(x), (v(-x) = -v(x)), in the context of supersymmetric quantum mechanical
models. By solving this eigenvalue problem with the help of known exactly
solvable potentials, we construct several classes of functions satisfying
certain orthogonality relations. We call them the Dunkl-supersymmetric
(Dunkl-SUSY) orthogonal functions. These functions can be expressed in terms of
the classical orthogonal polynomials (COPs). The key feature of these functions
is that they appear by pairs, i.e., Qn(x) and Qn(-x) are both the
eigenfunctions of L. A general formulation of the Dunkl-SUSY orthogonal
polynomials is also presented.
