Approximation by Delta-Convex Mappings in Certain Spaces. (25th January 2022) - Kashimoto, M. S.
Abstract: Let Y and E be real normed spaces, Ω a convex subset of Y, and D C ( Ω ; E ) the class of all continuous delta-convex mappings on Ω . We provide a proof of the density of D C ( Ω ; E ) in the space of continuous mappings C ( Ω ; E ) endowed with the compact-open topology. Under certain conditions on Ω and E, we also show the density of D C ( Ω ; E ) ∩ A in A when A = C b ( Ω ; E ) and A = C k ( Ω ; E ) with respect to the strict topology and to the compact-open topology of order k, respectively.