  In this paper, we establish the conditional Hyers-Ulam-Rassias stability of
the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s
g(x) + t h(y)$ on various restricted domains such as inside balls, outside
balls, and punctured spaces. In addition, we prove the orthogonal stability of
this equation and study orthogonally generalized Jensen mappings on Balls in
inner product spaces.
