We investigate the approximation of the Monge problem (minimizing ∫ Ω |T (x)− x|dμ(x) among the vector-valued maps T with prescribed image measure T#μ) by adding a vanishing Dirichlet energy, namely ε ∫ Ω |DT |. We study the Γ-convergence as ε → 0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we a...

For strongly competitive discrete-time dynamical systems on a strongly ordered topological vector space, it is proved that any αor ω-limit set is unordered and lies on some invariant hypersurface with codimension one, which generalizes Hirsch’s results for competitive autonomous systems of ordinary differential equations to competitive maps in a very general framework and implies the Sarkovskii...

An important well-known result of Rota describes the relationship between the Möbius functions of two posets related by a Galois connection. We present an analogous result relating the antipodes of the corresponding incidence Hopf algebras, from which the classical formula can be deduced. To motivate the derivation of this more general result, we first observe that a simple conceptual proof of ...

Proof of Lemmas A.2 and A.1. {Λi}i is an equilibrium if and only if {Λi}i = F ({Λi}i). By direct calculation, defining Xi = (Λi + αiVN(i)), we get {Λi}i = F ({Λi}i) if, and only if, {Xi}i = G({Xi}i). That F and G are monotone increasing follows because matrix inversion Y → Y −1 is monotone decreasing (e.g., Horn and Johnson (2013)), and projection onto N(i) Y → YN(i) is monotone increasing in t...

We prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problem over a general closed convex set. Sufficient conditions for the strong monotonicity of their perturbed versions are also shown. These results include some known ones in the literature as particular instances. Inspired by these results, we ...

Let S be a non empty set and let a, b be elements of S. The functor a, b, ... yields a function from N into S and is defined by the condition (Def. 1). (Def. 1) Let i be a natural number. Then (i) if there exists a natural number k such that i = 2 ·k, then (a, b, ...)(i) = a, and (ii) if it is not true that there exists a natural number k such that i = 2 ·k, then (a, b, ...)(i) = b. We now stat...

This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de…ned on spaces of random variables, possibly with the so-called Fatou property. We show …rst that the celebrated Namioka-Klee theorem for linear, positive functionals holds also for convex monotone maps on Frechet lattices. It is well-known among the specialists th...

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy o...

It is shown that pseudomonotone and quasimonotone maps can be characterized by a first order property provided they are regular. This result extends the well known characterization of nonvanishing generalized monotone maps to an essentially larger class. The paper supplements a recent contribution by Crouzeix and Ferland (1996) and solves a related open problem concerning homogeneous excess dem...