Approximation by Delta-Convex Mappings in Certain Spaces. (25th January 2022)

• Record Type: Journal Article
• Authors: Kashimoto, M. S.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 2(2022)
• Page Start: 168
• Page End: 180
• Publication Date: 2022-01-25
• Subjects: Delta-convex mappings -- Kakutani-Stone theorem -- polynomial algebra -- strict topology; primary 41A65 -- secondary 46E40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2021420
• Languages: English
• ISSNs: 0163-0563

Abstract

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.