Stability results for convergence of convex sets and functions in nonreflexive spaces

Abstract

Let $\Gamma(X)$ be the convex proper lower semicontinuous functions on a normed linear space $X$. We show, subject to Rockafellar's constraints qualifications, that the operations of sum, episum and restriction are continuous with respect to the slice topology that reduces to the topology of Mosco convergence for reflexive $X$. We show also when $X$ is complete that the epigraphical difference is continuous. These results are applied to convergence of convex sets