  We prove a remarkable generalization of a convexity theorem for semisimple
symmetric spaces G/H established earlier in 1986 by the second named author.
The latter result generalized Kostant's non-linear convexity theorem for the
Iwasawa decomposition of a real semisimple Lie group.
  The present generalization involves Iwasawa decompositions related to minimal
parabolic subgroups of G of arbitrary type instead of the particular type
relative to H considered in 1986.
