C-Extreme Points and C-Faces of the Epigraph of C-Ane Maps in -Rings

In this paper, we define the notion of C-ane maps in the unital -rings and we investigate the C-extreme points of the graph and epigraph of such maps. We show that for a C-convex map f defined on a unital -ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C-face of the epigraph of f . Moreover, we prove some results about the C-faces of C-convex sets in -rings.