Results 111 to 120 of about 498,513 (254)

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  

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

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

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

Best proximity point for weak cyclic Kannan type $F-$contraction map and cyclic Chatterjea type $F-$contraction map

Ratio Mathematica
In this paper, we introduce an innovative category of contractions termed "cyclic Chatterjea type $F-$contraction" and "weak cyclic Kannan type $F-$contraction." Subsequently, we establish a theorem for determining the best proximity point in a uniformly
Satyaj Tiwari, Monika Dewangan
doaj   +1 more source

Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory

Journal of Function Spaces and Applications, 2004
We present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a ...
Peter G. Dodds, Theresa K. Dodds, Alexander A. Sedaev, Fyodor A. Sukochev   +3 more
doaj   +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  

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

Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces

Journal of Applied Mathematics, 2014
We consider the variational inequality problem for a family of operators of a nonempty closed convex subset of a 2-uniformly convex Banach space with a uniformly Gâteaux differentiable norm, into its dual space.
Yasunori Kimura, Kazuhide Nakajo
doaj   +1 more source

Simultaneously continuous retraction and Bishop-Phelps-Bollob\'as type theorem [PDF]

, 2014
We study the existence of a retraction from the dual space $X^*$ of a (real or complex) Banach space $X$ onto its unit ball $B_{X^*}$ which is uniformly continuous in norm topology and continuous in weak-$*$ topology.
Han Ju Lee, Kim, Or X, Sun Kwang
core