Title: The proximal point algorithm in geodesic spaces with curvature bounded above,
Abstract: We investigate the asymptotic behavior of sequences generated by the proximal
point algorithm for convex functions in complete geodesic spaces with curvature
bounded above. Using the notion of resolvents of such functions, which was
recently introduced by the authors, we show the existence of minimizers of
convex functions under the boundedness assumptions on such sequences as well as
the convergence of such sequences to minimizers of given functions.