c*-extreme points and c*-faces of the epigraph if c*-affine maps in *-rings

Abstract. in this paper, we define the notion of c*-affine 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 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.