Results 11 to 20 of about 1,086,676 (318)
Cascading Operators in CAT(0) Spaces [PDF]
Axioms, 2021 In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps.
Helga Fetter Nathansky +1 more
doaj +2 more sources
arXiv, 2011 We investigate various notions of rough CAT(0). These conditions define classes of spaces that strictly include the union of all Gromov hyperbolic length spaces and all CAT(0) spaces.
Buckley, S.M., Falk, K.
arxiv +6 more sources
Curtain Model for CAT(0) Spaces and Isometries [PDF]
arXiv, 2023 This paper studies the dynamics of isometries in the curtain model, which is used to capture the hyperbolicity in a fixed CAT(0) space. We establish several fundamental properties, fully classify the behavior of semisimple isometries of a CAT(0) space in the associated curtain model, and prove that an isometry is contracting in a CAT(0) space if and ...
Yutong Chen
arxiv +3 more sources
Tits compact CAT(0) spaces [PDF]
arXiv, 2011 We investigate CAT(0) metric spaces whose associated Tits boundary is compact. Prominent examples of such spaces are of course the euclidean ones. However there exist non trivial geodesically complete CAT(0) spaces with compact Tits boundary that are far from being flat.
Aurélien Bosché
arxiv +3 more sources
The Boundary at Infinity of a Rough CAT(0) Space
Analysis and Geometry in Metric Spaces, 2014 We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces.
Buckley S.M., Falk K.
doaj +4 more sources
Strong Convergence of an Implicit Algorithm in CAT(0) Spaces [PDF]
Fixed Point Theory and Applications, 2010 AbstractWe establish strong convergence of an implicit algorithm to a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive maps in CAT"Equation missing" spaces. Our work improves and extends several recent results from the current literature.
Abdul Aziz Domlo +2 more
openaire +6 more sources
On Approximating Fixed Point in CAT(0) Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we obtain a new modified iteration process in the setting of CAT(0) spaces involving generalized $\alpha$-nonexpansive mapping. We prove strong and $\Delta$ convergence results for approximating fixed point via newly defined iteration ...
Chanchal Garodia, Izhar Uddin
doaj +3 more sources
CAT(0) spaces with polynomial divergence of geodesics [PDF]
Geometriae Dedicata, Online First, July 2012, 2011 We construct a family of finite 2-complexes whose universal covers are CAT(0) and have polynomial divergence of desired degree. This answers a question of Gersten, namely whether such CAT(0) complexes exist.
arxiv +6 more sources
On the Monotone Mappings in CAT(0) Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods by combining the resolvent method with Halpern's iterative method and viscosity approximation method for finding a ...
Davood Afkhami Taba, Hossein Dehghan
doaj +3 more sources
A quadratic rate of asymptotic regularity for CAT(0)-spaces
Journal of Mathematical Analysis and Applications, 2007 In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a ...
Laurentiu Leustean, Laurentiu Leustean
openaire +5 more sources