  We consider generalizations of the $BC$-type relativistic
Calogero-Moser-Sutherland models, comprising of the rational, trigonometric,
hyperbolic, and elliptic cases, due to Koornwinder and van Diejen, and
construct an explicit eigenfunction for these generalizations. In special
cases, we find the various kernel function identities, and also a
Chalykh-Feigin-Sergeev-Veselov type deformation of these operators and their
corresponding kernel functions, which generalize the known kernel functions for
the Koornwinder-van Diejen models.
