Monotonicidade maximal de bifunções

Abstract

In this dissertation, we study the relationships between Maximally Monotone Operators and Maximally Monotone Bifunctions established by the authors Nicholas Hadjisavvas, Flávia Morgana O. Jacinto and Juan Enrique Martínez-Legaz. In addition, we also established the relationship between bifunctions and operators via the new concept of maximally monotonicity for bifunctions called Pointwise Maximally Monotonicity (PMMB). It was also addressed the definition of Fitzpatrick function associated with an operator, whose properties were presented, in the form of examples, wich motivated the definition and study of the Fitzpatrick Transform for a bifunction. We conclude by establishing that the Fitzpatrick Transform of a Bifunction coincides with the Fitzpatrick function of an operator when both are conveniently defined satisfying special properties. It should be noted that we adressed some elements of convex analysis and of the theory of conjugation to substantiate the results presented in this work.