Two modified proximal point algorithms in geodesic spaces with curvature bounded above

We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.Comment: 22 pages; some minor corrections were mad

The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings

In this paper we provide a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results in this direction proved recently in spaces of curvature bounded above. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings in the setting of $p$-uniformly convex geodesic spaces focusing on asymptotic regularity and convergence results