Related papers: Quantization Errors, Human--AI Interaction, and Ap…

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…

We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $\mathrm L^p$ measure equivalence. In this paper, our main focus will be on amenable…

For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

We introduce asymptotic-M\"obius (AM) maps, a large-scale analogue of quasi-M\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of…

This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…

We show a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic…

Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…

In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Espinola on approximate fixed points of nonexpansive mappings in product spaces $(C\times M)_\infty$, where M is a metric…

We provide a tool for studying properly discontinuous actions of non-compact groups on locally compact, connected and paracompact spaces, by embedding such an action in a suitable zero-dimensional compactification of the underlying space…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…

In this paper, we study the local convergence of the standard ADMM scheme for a class of nonconvex composite problems arising from modern imaging and machine learning models. This problem is constrained by a closed convex set, while its…

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.…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

A well-known result of W. Ray asserts that if $C$ is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping $T$: $C\to C$ that has no fixed point. In this paper we establish some common fixed point properties…

We present a head-to-head evaluation of the Improved Inexact--Newton--Smart (INS) algorithm against a primal--dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method…

This survey reviews results on harmonic maps into spaces of non-positive curvature, with a focus on targets that lack smooth structure. More precisely, we consider targets that are complete metric spaces with non-positive curvature in the…