Let Λ be a complete metric space, and let {Sλ(·) : λ ∈ Λ} be a parametrised family of semigroups with global attractors Aλ. We assume that there exists a fixed bounded set D such that Aλ ⊂ D for every λ ∈ Λ. By viewing the attractors as the limit as t → ∞ of the sets Sλ(t)D, we give simple proofs of the equivalence of ‘equi-attraction’ to continuity (when this convergence is uniform in λ) and s...

In this paper, the relationships between semicontinuity and preinvexity of fuzzy mappings are investigated. The concepts of intermediate-point preinvex fuzzy mappings and weakly preinvex fuzzy mappings are first introduced, and the authors establish a characterization for a weakly preinvex fuzzy mapping in terms of its epigraph. In this context, a characterization of a preinvex fuzzy mapping in...

A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.

Abstract: We provide a new proof of the upper-semicontinuity property for the global attractors admitted by the solution operators associated with some strongly damped wave equations. In particular, we demonstrate an explicit control over semidistances between trajectories in the weak energy phase space in terms of the perturbation parameter. This result strengthens the recent work by Y. Wang a...

The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one. This result is applied to the stochastic Reaction-Diffusion with white noise defined on the entire space Rn.

In an environment in which the primitive is the space of distribution functions, we characterize the quantile functions by the axioms ordinal covariance, monotonicity with respect to …rst order stochastic dominance, and upper semicontinuity. We show how to characterize the VaR in a similar manner.

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonia...

In this paper we prove an upper semicontinuity result for perturbations of cocycle attractors. In particular, we study relationship between non-autonomous and global attractors. In this sense, we show that the concept of a cocycle attractor is a sensible generalization to non-autonomous and random dynamical systems of that of the global attractor.

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative respect to a left-continuous non-decreasing function replaces classical derivative. The involved set-valued mapping is not assumed have compact and convex values, nor be upper semicontinuous concerning second argument everywhere, as in other related works. A condition involving c...