On the sum rules and maximality of generalized subdifferentials

Some properties of sigma-convex functions are studied. Then some relations between the notions of sigma-subdifferentials and sigma-convex functions are established. Also, we present some results regarding the sum formula for the sigma-subdifferential. Moreover, we obtain some particular relationships between the sigma-subdifferential and the (sigma, y)-conjugate. Finally, by imposing some assumptions on f and sigma, the maximal 2 sigma-monotonicity of sigma-subdifferential is studied. Indeed, the maximality of the usual Fenchel subdifferentials of lower semi-continuous convex functions follows from our result.