Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces

We give rates of strong convergence for the proximal point algorithm PPA computing the unique zero z of operators A in uniformly convex Banach spaces which are uniformly accretive at z. We also get a rate of convergence to some zero of A if A has a modulus of regularity. In the boundedly compact case, we obtain a rate of metastability of PPA in the sense of Tao for arbitrary accretive operators A (satisfying a range condition so that the PPA is well-defined).