5 citations · 15 across the 13 of their papers we have counts for
22 papers
Basic convex analysis in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however…
Local linear convergence of alternating projections in metric spaces with bounded curvature
Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, eq…
Geodesic rays, the "Lion-Man" game, and the fixed point property
Genaro López-Acedo, Adriana Nicolae, Bożena Piątek
This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point prope…
A uniform betweenness property in metric spaces and its role in the quantitative analysis of the "Lion-Man" game
Ulrich Kohlenbach, Genaro López-Acedo, Adriana Nicolae
In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betwee…
"Lion-Man" and the Fixed Point Property
Genaro López-Acedo, Adriana Nicolae, Bożena Piątek
This paper focuses on the relation between the fixed point property for continuous mappings and a discrete lion and man game played in a strongly convex domain. Our main result sta…
An abstract proximal point algorithm
Laurentiu Leustean, Adriana Nicolae, Andrei Sipos
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of none…
Moduli of regularity and rates of convergence for Fejér monotone sequences
Ulrich Kohlenbach, Genaro López-Acedo, Adriana Nicolae
In this paper we introduce the concept of modulus of regularity as a tool to analyze the speed of convergence, including the finite termination, for classes of Fejér monotone seque…
Barycenters in uniformly convex geodesic spaces
Laurentiu Leustean, Adriana Nicolae, Alexandru Zaharescu
This note proves a result on the existence of barycenters in a class of uniformly convex geodesic spaces.
Proximal minimization in CAT spaces
Rafa Espínola, Adriana Nicolae
In this note, we provide convergence results for the proximal point algorithm and a splitting variant thereof in the setting of CAT spaces with using a recent definitio…
Quantitative asymptotic regularity results for the composition of two mappings
Ulrich Kohlenbach, Genaro Lopez-Acedo, Adriana Nicolae
In this paper, we use techniques which originate from proof mining to give rates of asymptotic regularity and metastability for a sequence associated to the composition of two firm…
A note on an alternative iterative method for nonexpansive mappings
Laurentiu Leustean, Adriana Nicolae
In this note we point out that results on the asymptotic behaviour of an alternative iterative method are corollaries of corresponding results on the well-known Halpern iteration.
Continuous Selections of Lipschitz Extensions in Metric Spaces
Rafa Espínola, Adriana Nicolae
This paper deals with the study of parameter dependence of extensions of Lipschitz mappings from the point of view of continuity. We show that if assuming appropriate curvature bou…
Quantitative results on Fejer monotone sequences
Ulrick Kohlenbach, Laurentiu Leustean, Adriana Nicolae
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the converge…
The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings
David Ariza-Ruiz, Genaro López-Acedo, Adriana Nicolae
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 direct…
A note on an ergodic theorem in weakly uniformly convex geodesic spaces
Laurentiu Leuştean, Adriana Nicolae
Karlsson and Margulis proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that focuses on th…
What do `convexities' imply on Hadamard manifolds?
Alexandru Kristály, Chong Li, Genaro Lopez +1
Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard ma…
Effective results on compositions of nonexpansive mappings
Laurentiu Leustean, Adriana Nicolae
This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the set…
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces
Aurora Fernandez Leon, Adriana Nicolae
Given and two nonempty subsets in a metric space, a mapping is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A,…
Effective results on nonlinear ergodic averages in CAT spaces
Laurentiu Leustean, Adriana Nicolae
In this paper we apply proof mining techniques to compute, in the setting of CAT spaces (with ), effective and highly uniform rates of asymptotic regularity and metastabi…
Averaged alternating reflections in geodesic spaces
Aurora Fernandez-Leon, Adriana Nicolae
We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibi…
Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
Adriana Nicolae
We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods o…
Mutually nearest and mutually farthest points of sets in geodesic spaces
Rafa Espinola, Adriana Nicolae
Let and be nonempty, bounded and closed subsets of a geodesic metric space . The minimization (resp. maximization) problem denoted by (resp. )…