  We establish the convergence of the forward-backward splitting algorithm
based on Bregman distances for the sum of two monotone operators in reflexive
Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has
so far been proved only in the case of minimization problems. The proposed
framework features Bregman distances that vary over the iterations and a novel
assumption on the single-valued operator that captures various properties
scattered in the literature. In the minimization setting, we obtain rates that
are sharper than existing ones.
