Uniform convergence on spaces of multifunctions
Uniqueness and non uniqueness of optimal maps in mass transport problem with not strictly convex cost
In the setting of the optimal transportation problem we provide some conditions which ensure the existence and the uniqueness of the optimal map in the case of cost functions satisfying mild regularity hypothesis and no convexity or concavity assumptions.
Upper quasi continuous maps and quasi continuous selections
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form , where is open and , are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form .
Useful properties of index pairs for upper semicontinuous multivalued dynamical systems.