Let \(p\in \mathbb {N}\) , Y be a real vector metric space and K be a closed convex cone in Y satisfying \(K\cap (-K)=\{0\}\) . We prove that a K-p-multiadditive s.v. map \(F:\mathbb {R}^p\rightarrow n(Y)\) which is K-continuous with respect to each coordinate, or K-measurable in the sense of Lebesgue/Baire, is K-continuous on the whole domain, and we give an explicit formula of such s.v. maps. These results generalize well-known results for multiadditive real functions from [15, Chapter 13.4]. Additionally, we consider the extension problem for solutions of conditional equations of K-multiadditive s.v. maps.
