Approximation semigroups for resolvent maps

In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex geodesic metric space. For our study, we introduce the notion of (general) resolvent maps which is a generalization of the resolvent maps in Lawson (J Lie Theory 33, 361–376, 2023) and then we prove several useful properties for the resolvent map and construct the approximation semigroups for resolvent maps. We also study the convergence of a proximal point like algorithm for the general resolvent map.