Let P ,X and Y be Banach spaces. Suppose that f : P ×X → Y is continuously Fréchet differentiable function depend on the point (p, x) and F : X ⇒ 2 is a set-valued mapping with closed graph. Consider the following parametric generalized equation of the form: 0 ∈ f(p, x) + F (x). (1) In the present paper, we study an extended Newton-type method for solving parametric generalized equation (1). In...

This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost bi-Lipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but ‘almost homogeneous’. We therefore study the problem of embedding an almost homogeneous subset ...

Based on the notion of Minimizing Lipschitz Extensions and its connection with the infinity Laplacian, a theoretical and computational framework for geometric nonrigid surface warping, and in particular the nonlinear registration of brain imaging data, is presented in this paper. The basic concept is to compute a map between surfaces that minimizes a distortion measure based on geodesic distanc...

For all μ > 0, a locally Lipschitz continuous map f with xf (x) > 0, x ∈ R\{0}, is constructed, such that the scalar equation ẋ (t) = −μx (t)−f (x (t− 1)) with delayed negative feedback has an infinite number of periodic orbits. All periodic solutions defining these orbits oscillate slowly around 0 in the sense that they admit at most one sign change in each interval of length of 1. Moreover, i...

Abstract We establish a new local well-posedness result in the space of finite Borel measures for mild solutions of the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two dimensions. Our result only requires that the initial measure satisfy the necessary assumption max x∈R μ({x}) < 8π. This work improves the small-data results of Biler [4] and the existence res...

A. In this note we give new characterizations of metric trees and Gromov hyperbolic spaces and generalize recent results of Chatterji and Niblo. Our results have a purely metric character, however, their proofs involve two classical tools from analysis: Stokes’ formula in R2 and a Rademacher type differentiation theorem for Lipschitz maps. This analytic approach can be used to give chara...

In this paper we investigate under which conditions the composition of two set-valued maps enjoys the linear openness property. To obtain our results, we use the Nadler’s fixed point theorem, and Lim’s lemma which provides an estimate for the distance between the sets of fixed points of two (set-valued) contractions. As an application, we obtain the Lipschitz property of the implicit solution m...

In this paper we prove the differentiability of Lipschitz maps X → V , where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direct...

Euclidean rotations in Rn are bijective and isometric maps. Nevertheless, they lose these properties when digitized in Zn. For n = 2, the subset of bijective digitized rotations has been described explicitly by Nouvel and Rémila and more recently by Roussillon and Cœurjolly. In the case of 3D digitized rotations, the same characterization has remained an open problem. In this article, we propos...