Convergence of set-valued mappings: Equi-outer semicontinuity (Q5961471)

The authors introduce the notion of equi-semicontinuity for collections of set-valued mappings of a topological space into a metric space. They investigate the equi-outer semicontinuity with the connection of the Choquet-Wijsman convergence of sets and with other convergence concepts for set-valued mappings as the Mosco graph-convergence. As a corollary of the investigation of uniform convergence the authors obtain the Arzelà-Ascoli theorem. Some interesting applications concerning the pointwise convergence of subgradient mappings, pointwise limits of maximal monotone operators defined on a Hilbert space and concerning differential inclusions are also included.