相关论文: Quantitative Characterizations of Regularity Prope…

We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…

We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent…

It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties…

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…

We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

We provide a characterization of r-regular sets in terms of the Lipschitz regularity of normal vector fields to the boundary.

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…

We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…

In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…

In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…

We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.

In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by…