Normal Characterization of the Main Classes of Quasiconvex Functions

In this article we explore the concept of the normal cone to the sublevel sets (or strict sublevel sets) of a function. By slightly modifying the original definition of Borde and Crouzeix, we obtain here a new (but strongly related to the already existent) notion of a normal operator. This technique turns out to be appropriate in Quasiconvex Analysis since it allows us to reveal characterizations of the various classes of quasiconvex functions in terms of the generalized quasimonotonicity of their `normal' multifunctions.

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