Selections and approximations of convex-valued equivariant mappings

Abstract

We present some abstract theorems on the existence of selections and graph-approximations of set-valued mappings with convex values in the equivariant setting, i.e. maps commuting with the action of a compact group. Some known results of the Michael, Browder and Cellina type are generalized to this context. The equivariant measurable as well as Carathéodory selection/approximation problems are also studied.