Approximate endpoints for set-valued contractions in metric spaces.
The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with is the limit of an approximate inverse system of metric polyhedra of . A completely metrizable separable space with is the limit of an...
Mostriamo che se è uno spazio metrico completo, allora è completa anche la metrica , indotta in modo naturale da sul sottospazio degli insiemi sfocati («fuzzy») di dati dalle quantità approssimate. Come è ben noto, è una metrica molto interessante nella teoria dei punti fissi di applicazioni sfocate, poiché permette di ottenere risultati soddisfacenti in questo contesto.
This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...