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

Cyclic Projections in Hadamard Spaces

We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Bačák. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular

Cyclic projections in Hadamard spaces

We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Ba\v{c}\'ak. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular.Comment: 6 pages, 3 figure

The computational content of super strongly nonexpansive mappings and uniformly monotone operators

Recently, Liu, Moursi and Vanderwerff have introduced the class of super strongly nonexpansive mappings as a counterpart to operators which are maximally monotone and uniformly monotone. We give a quantitative study of these notions in the style of proof mining, providing a modulus of super strong nonexpansiveness, giving concrete examples of it and connecting it to moduli associated to uniform monotonicity. For the supercoercive case, we analyze the situation further, yielding a quantitative inconsistent feasibility result for this class (obtaining effective uniform rates of asymptotic regularity), a result which is also qualitatively new