  Projective splitting is a family of methods for solving inclusions involving
sums of maximal monotone operators. First introduced by Eckstein and Svaiter in
2008, these methods have enjoyed significant innovation in recent years,
becoming one of the most flexible operator splitting frameworks available.
While weak convergence of the iterates to a solution has been established,
there have been few attempts to study convergence rates of projective
splitting. The purpose of this paper is to do so under various assumptions. To
this end, there are three main contributions. First, in the context of convex
optimization, we establish an $O(1/k)$ ergodic function convergence rate.
Second, for strongly monotone inclusions, strong convergence is established as
well as an ergodic $O(1/\sqrt{k})$ convergence rate for the distance of the
iterates to the solution. Finally, for inclusions featuring strong monotonicity
and cocoercivity, linear convergence is established.
