  We obtain new concavity results, up to a suitable transformation, for a class
of quasi-linear equations in a convex domain involving the $p$-Laplace operator
and a general nonlinearity satisfying concavity type assumptions. This provides
an extension of results previously known in the literature only for the torsion
and the eigenfunction equations. In the semilinear case $p = 2$ the results are
already new since they include new admissible nonlinearities.
