Monotone Bifunctions and Monotone Operators

Our purpose is to study and advance in the research area of monotone and generalized monotone operators and bifunctions. To each bifunction we will correspond an operator and for every operator will correspond a bifunction. We also show that each monotone operator is “inward locally bounded” at every point of the closure of its domain, a property which collapses to ordinary local boundedness at interior points of the domain. Moreover, we derive some properties of cyclically monotone bifunctions. A considerable part of this thesis is devoted to introducing and studying of the “Fitzpatrick transform of a bifunction” and its properties. Whenever the monotone bifunction is lower semi-continuous and convex with respect to its second variable, the Fitzpatrick transform permits to obtain results on its maximal monotonicity