In mathematics generalization is one of the main activities of researchers. It opens up new theoretical horizons and broadens the ?elds of applications. Intensive study of generalized convex objects began about three decades ago when the theory of convex analysis nearly reached its perfect stage of devel- ment with the pioneering contributions of Fenchel, Moreau, Rockafellar and others. The involvement of a number of scholars in the study of generalized convex functions and generalized monotone operators in recent years is due to the quest for more general techniques that are able to describe...