Douglas–Rachford method
For two proximal
maps Pf,Ph,
define reflected
maps Rf=2Pf−I and
Rh=2Ph−I. The Douglas--Rachford
fixed-point map is
T=21(I+RfRh)=I−Ph+Pf(2Ph−I).
Because reflected proximal
maps are nonexpansive,
T is firmly nonexpansive.