We present a brief survey on two classes of single-valued and multivalued maps: the paramonotone maps and the pseudomonotone* maps. The former concept was introduced for the rst time in [5], the latter in [7] and it was slightly modied in [10]. These two concepts permit to characterize in a stronger way convex and pseudoconvex functions. Moreover pseudomonotone* maps are characterized by the cutting plane property in a sense. Lastly we present a possible extension of the notion of pseudomonotone* maps to the equilibrium bifunctions and we show that they have the cutting property.
On paramonotone and pseudomonotone* maps
CASTELLANI, MARCO;GIULI, MASSIMILIANO
2009-01-01
Abstract
We present a brief survey on two classes of single-valued and multivalued maps: the paramonotone maps and the pseudomonotone* maps. The former concept was introduced for the rst time in [5], the latter in [7] and it was slightly modied in [10]. These two concepts permit to characterize in a stronger way convex and pseudoconvex functions. Moreover pseudomonotone* maps are characterized by the cutting plane property in a sense. Lastly we present a possible extension of the notion of pseudomonotone* maps to the equilibrium bifunctions and we show that they have the cutting property.File in questo prodotto:
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