Approaching the Maximal Monotonicity of Bifunctions via Representative Functions

We provide an approach to maximal monotone bifunctions based on the theory of representative functions. Thus we extend to nonreflexive Banach spaces recent results due to A. N. Iusem ["On the maximal monotonicity of diagonal subdifferential operators", J. Convex Analysis 18 (2011) 489–503] and, respectively, to N. Hadjisavvas and H. Khatibzadeh ["Maximal monotonicity of bifunctions", Optimization 59 (2010) 147–160], where sufficient conditions guaranteeing the maximal monotonicity of bifunctions were introduced. New results involving the sum of two monotone bifunctions are also presented.