Related papers: Weakly convex sets and modulus of nonconvexity

The aim of this paper is to introduce an algebraic structure on the set of all coalgebras with the same state space over the given type which allows us to present definitions of weak and delay bisimulation for coalgebras. Additionally, we…

In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space $X$ coarsely (resp. uniformly) embeds into a Banach space $Y$…

If $(X,d)$ is a metric space then the map $f\colon X\to X$ is defined to be a weak contraction if $d(f(x),f(y))<d(x,y)$ for all $x,y\in X$, $x\neq y$. We determine the simplest non-closed sets $X\subseteq \mathbb{R}^n$ in the sense of…

We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our…

In this paper, we define weakly coherent rings, and examine the transfer of these rings to homomorphic image, trivial ring extension, localization, and direct product. These results provide examples of weakly coherent rings that are not…

The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling…

A multi-objective optimization problem is $C^r$ weakly simplicial if there exists a $C^r$ surjection from a simplex onto the Pareto set/front such that the image of each subsimplex is the Pareto set/front of a subproblem, where $0\leq r\leq…

The main problem considered in the present paper is to single out classes of convex sets, whose convexity property is preserved under nonlinear smooth transformations. Extending an approach due to B.T. Polyak, the present study focusses on…

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…

In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed…

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…

A wide new class of subsets of a Banach space $X$ named coarse $p$-limited sets ($ 1\leq p < \infty$) is introduced by considering weak* $p$-summable sequences in $X'$ instead of weak* null sequences. We study its basic properties and…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous…

The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of weak…

Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…

A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are…

It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty…

In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

We show that groups with a mild form of non-positive curvature (a navigable path system) satisfy the weak rank rigidity conjecture: they either have linear divergence or a Morse element. This class includes discrete groups of projective…