Epi-distance convergence of parametrised sums of convex functions in non-reflexive spaces

A weakened set of conditions is established for the epi-distance convergence of a sum {f(v) + g(v)}(v is an element ofW) of parameterised closed convex functions {f(v)}(v is an element ofW) and {g(v)}(v is an element ofW) for v --> w, on an arbitrary Banach space. They are as follows. (1) 0 is an element of sqri(dom f(w) - dom g(w)); and (2) X-w := cone(dom f(w) - dom g(w)) has closed algebraic complement Y-w; and (3) X-v boolean AND Y-w = {0} for all v near w, (where X-v := (span) over bar (dom f(v) - dom g(v))). These are motivated by similar interiority conditions found in Fenchel duality theory. Our results are then used to investigate saddle-point convergence in Young-Fenchel duality in which both functions vary in a very general fashion.