  The theory of monotone operators plays a major role in modern optimization
and many areas of nonlinera analysis. The central classes of monotone operators
are matrices with a positive semidefinite symmetric part and subsifferential
operators. In this paper, we complete our study to the displacement mappings.
We derive formulas for set-valued and Moore-Penrose inverses. We also give a
comprehensive study of the the operators ($(1/2) {\rm Id} + T$ and its inverse)
and provide a formula for $((1/2) {\rm Id} + T)^{-1}$. We illustrate our
results by considering the reflected and the projection operators to closed
linear subspaces.
