Results 71 to 80 of about 476,682 (147)

Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees

, 2015
We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly closed ...
Neumann, Eike
core   +1 more source

Convergence and nonconvergence in a nonlocal gradient flow

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract We study the asymptotic convergence as t→∞$t\rightarrow \infty$ of solutions of ∂tu=−f(u)+∫f(u)$\partial _t u=-f(u)+\int f(u)$, a nonlocal differential equation that is formally a gradient flow in a constant‐mass subspace of L2$L^2$ arising from simplified models of phase transitions. In case the solution takes finitely many values, we provide
Sangmin Park, Robert L. Pego
wiley   +1 more source

Coarse embedding into uniformly convex Banach space [PDF]

arXiv, 2011
In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly relative hyperbolic to a subgroup $H$, we proved that if $H$ admits a coarse embedding into a uniformly convex Banach ...
arxiv  

Fixed Point Theorem for Non-Expansive Mappings on Banach Spaces with Unifformly Normal Structure [PDF]

, 1977
In [1] Kirk proved that if D is a bounded, closed, and convex subset of a reflexive Banach space that has normal structure, then every non-expansive mapping of D into D has a fixed point.
Gillespie, A. A., Williams, B. B.
core   +1 more source

ℓp$\ell ^p$ metrics on cell complexes

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Motivated by the observation that groups can be effectively studied using metric spaces modelled on ℓ1$\ell ^1$, ℓ2$\ell ^2$ and ℓ∞$\ell ^\infty$ geometry, we consider cell complexes equipped with an ℓp$\ell ^p$ metric for arbitrary p$p$. Under weak conditions that can be checked locally, we establish non‐positive curvature properties of these
Thomas Haettel, Nima Hoda, Harry Petyt
wiley   +1 more source

Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces [PDF]

, 2012
This article generalizes the work of Ballmann and \'Swiatkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.
arxiv   +1 more source

Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces [PDF]

, 2019
In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly ...
Reddy, B. Krishna, Takele, Mollalgn H.
core   +1 more source

Carnot rectifiability and Alberti representations

Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.
Abstract A metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability ...
G. Antonelli, E. Le Donne, A. Merlo
wiley   +1 more source

A uniformly convex hereditarily indecomposable Banach space [PDF]

arXiv, 1995
A {\em hereditarily indecomposable (or H.I.)} Banach space is an infinite dimensional Banach space such that no subspace can be written as the topological sum of two infinite dimensional subspaces. As an easy consequence, no such space can contain an unconditional basic sequence.
arxiv  

Smooth norms and approximation in Banach spaces of the type C(K)

, 2006
We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, then all continuous real-valued functions on C(K) may be uniformly ...
Hajek, Petr, Haydon, Richard
core   +2 more sources