Duality for the sum of convex functions in general normed spaces (Q1337813)

A new condition ensuring that the conjugate of a sum of two convex functions is equal to the exact epigraphical sum of their conjugates is given. It encompasses the classical Moreau-Rockafellar condition [\textit{R. T. Rockafellar}, Duke Math. J. 33, 81-89 (1966; Zbl 0138.093)] and the Attouch-Brezis one [\textit{H. Attouch} and \textit{H. Brezis}, Aspects of mathematics and its applications, Collect. Pap. Hon. L. Nachbin, 125-133 (1986; Zbl 0642.46004)]. Applications are given to stability in convex duality and to lower semicontinuity of the epigraphical sum of convex functions.