Continuous selection theorems for nonlower semicontinuous multifunctions. (Q1413168)

This paper is motivated by \textit{A. L. Brown}'s paper [J. Approximation Theory 57, 48--68 (1989; Zbl 0675.41037)], where necessary and sufficient conditions were found in order that a convex-set valued multifunction be lower semicontinuous. The main results of this paper extend that of Brown to the case when the multifunction has either C-convex values in \(C(S,\mathbb R^n)\) or L-convex values in \(L^\infty(T,\mathbb R^n)\). It is also shown that a similar extension to \(L^1(T,\mathbb R^n)\) valued multifunctions is not valid in general.