
Journal of Convex Analysis 28 (2021), No. 1, 011018 Copyright Heldermann Verlag 2021 Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces Ulrich Kohlenbach Department of Mathematics, Technische Universität, Schlossgartenstrasse 7, 64289 Darmstadt, Germany kohlenbach@mathematik.tudarmstadt.de 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 welldefined). Keywords: Accretive operators, proximal point algorithm, uniformly convex Banach spaces, rates of convergence, metastability, proof mining. MSC: 47H05, 47J25, 03F10. [ Fulltextpdf (102 KB)] for subscribers only. 