R is any coupling function, replacing w(x) by ga(x, w). 13).
63), for example, those in which the coupling function ça takes only the values 0 and —oc (related to "quasi-subdifferentials"). 65) the subdifferential of f at x o with respect to the conjugation c(p) (or, briefly, the e(ço)-subdifferential of f at x 0 ), and we will also denote it by acm f (x0). 63)). 47) can be extended to arbitrary dualities A : R x —> R w , yielding a general "Fenchel—Young inequality" with respect to A. Since this definition of a° f (x0) is more technical, we will give it only in Chapter 10.
Abstract Convex Analysis (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) by Ivan Singer