  We investigate the symmetric Dunkl-classical orthogonal polynomials by using
a new approach applied in connection with the Dunkl operator.
  The main aim of this technique is to determine the recurrence coefficients
first and foremost. We establish the existence and uniqueness of symmetric
Dunkl-classical orthogonal polynomials, and also confirm that only two families
of orthogonal polynomials, that is, the generalized Hermite polynomials and the
generalized Gegenbauer polynomials, belong to this class. Two apparently new
characterizations in a more general setting are given. This paper complements
earlier work of Ben Cheikh and Gaied.
