GENERALIZED CONVEXITY OF FUNCTIONS AND GENERALIZED MONOTONICITY OF SET-VALUED MAPS

We establish connections between some concepts of generalized monotoni city for set-valued maps introduced earlier and some notions of genera lized convexity. Moreover, a notion of pseudomonotonicity for set-valu ed maps is introduced; it is shown that, if a function f is continuous , then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar .